MES Jr. Grade • 2024 • Paper-I
The electric lines of force enter or leave a charged surface at an angle
A)
depending upon surface condition
B)
30°
C)
60°
D)
90°
In electrostatics, the electric field (and thus the lines of force) at the surface of a conductor must be perpendicular to the surface. This is because any tangential component of the electric field would exert a force on the free electrons on the conductor's surface, causing them to move until the tangential component becomes zero. Once the system reaches electrostatic equilibrium, the net force on the surface charges is zero in the tangential direction, meaning the electric field vector is oriented exactly normal (perpendicular) to the surface. Therefore, the lines of force enter or leave the charged surface at an angle of 90°.
MES Jr. Grade • 2024 • Paper-I
At a temperature zero Kelvin, silicon material behaves as
A)
superconductor
B)
conductor
C)
insulator
D)
semiconductor
Step-by-step reasoning: 1. Silicon is an intrinsic semiconductor. In a semiconductor, the valence band is completely filled and the conduction band is empty at absolute zero (0 Kelvin). 2. For electrical conduction to occur, electrons must gain enough energy to jump across the energy gap (band gap) from the valence band to the conduction band. 3. At 0 K, there is no thermal energy available to excite electrons. Therefore, no electrons can move into the conduction band, and no holes are created in the valence band. 4. Since there are no free charge carriers (electrons or holes) available to move under the influence of an electric field, the material cannot conduct electricity. 5. A material that does not conduct electricity is defined as an insulator. Thus, at 0 K, silicon behaves as a perfect insulator. Other options: (a) Superconductors have zero electrical resistance, which is not the case for silicon; (b) Conductors have overlapping bands or partially filled bands; (d) While silicon is a semiconductor by nature, its 'behavior' at 0 K specifically is that of an insulator.
MES Jr. Grade • 2024 • Paper-I
Which of the following represents the Maxwell’s continuity equation for time varying electromagnetic fields
A)
∇·J + ∂ρ/∂t = 0
B)
∇·J = ρ
C)
∇×E = 0
D)
None of these
The continuity equation is a mathematical statement of the law of conservation of charge. It states that the current flowing out of a closed surface (divergence of current density J) must be equal to the rate of decrease of the charge enclosed within that surface.
Mathematically, the net current flowing out of a volume is given by the volume integral of the divergence of current density: ∫(∇·J)dV. According to the conservation of charge, this must equal the negative rate of change of total charge Q: -dQ/dt. Since Q = ∫ρdV, we have ∫(∇·J)dV = -∂/∂t ∫ρdV. For this to hold for any arbitrary volume, the integrands must be equal: ∇·J = -∂ρ/∂t, which rearranges to ∇·J + ∂ρ/∂t = 0.
Analysis of other options:
- Option (b) ∇·J = ρ is incorrect; it does not represent a standard physical law in electromagnetics.
- Option (c) ∇×E = 0 represents the electrostatic condition (where the electric field is conservative), but in time-varying fields, ∇×E = -∂B/∂t (Faraday's Law).
MES Jr. Grade • 2024 • Paper-I
When an EM wave is incident from a more dense medium to less dense medium at an angle equal to or exceeding the critical angle, the wave suffers
A)
total internal transmission
B)
total internal reflection
C)
total internal refraction
D)
none of these
The phenomenon described in the question is a fundamental principle of optics and electromagnetic wave propagation.
1. **Conditions for Total Internal Reflection (TIR):** For TIR to occur, two conditions must be met:
- The wave must travel from an optically denser medium (higher refractive index, n1) to an optically rarer/less dense medium (lower refractive index, n2).
- The angle of incidence must be equal to or greater than the critical angle (θc).
2. **The Critical Angle:** The critical angle is the angle of incidence for which the angle of refraction is 90°. According to Snell's Law (n1 sin θ1 = n2 sin θ2), when θ2 = 90°, sin θc = n2/n1.
3. **What happens at or above the critical angle:**
- If the angle of incidence is exactly the critical angle, the refracted ray grazes the boundary.
- If the angle of incidence exceeds the critical angle, the wave cannot pass into the second medium (refraction is impossible) and is instead reflected entirely back into the denser medium.
4. **Evaluating Options:**
- (a) Total internal transmission: Incorrect; the wave is prevented from transmitting into the second medium.
- (b) Total internal reflection: Correct; this is the defined term for this phenomenon.
- (c) Total internal refraction: Incorrect; refraction refers to the bending of light as it passes from one medium to another; here, it fails to pass through.
- (d) None of these: Incorrect.
MES Jr. Grade • 2024 • Paper-I
When the relative permeability of a material is much greater than 1, it is called
A)
diamagnetic material
B)
paramagnetic material
C)
ferromagnetic material
D)
none of these
Relative permeability (μr) is the ratio of the permeability of a material (μ) to the permeability of free space (μ₀). It indicates how easily a material can be magnetized.
1. Diamagnetic materials: These materials have a relative permeability slightly less than 1 (μr < 1). They are weakly repelled by a magnetic field.
2. Paramagnetic materials: These materials have a relative permeability slightly greater than 1 (μr ≈ 1, but > 1). They are weakly attracted to a magnetic field.
3. Ferromagnetic materials: These materials have a relative permeability much greater than 1 (μr >> 1), often in the hundreds or thousands. They exhibit strong magnetization and can retain magnetism (permanent magnets).
Since the question specifies that the relative permeability is 'much greater than 1', the correct classification is ferromagnetic.
MES Jr. Grade • 2024 • Paper-I
In a homogeneous p-n junction semiconductor
A)
the width of p and n layers are equal and constant throughout
B)
the impurity levels on both sides of the junctions are same
C)
same semiconductor materials is used on both sides of the junction
D)
different semiconductor materials are used on both sides of the junction
A p-n junction is called 'homogeneous' when the same base semiconductor material (e.g., Silicon or Germanium) is used for both the p-type and n-type regions. In such a device, the transition from p-type to n-type is achieved by doping the same crystal with different impurities, rather than joining two different semiconductor materials.
Analysis of options:
- Option (a) is incorrect because the width of the layers depends on the design of the specific device and is not a requirement for it to be 'homogeneous'.
- Option (b) is incorrect because the impurity levels (doping concentrations) can be different (e.g., one side can be heavily doped and the other lightly doped, as in a p+-n junction) while still being homogeneous.
- Option (c) is correct because 'homogeneous' refers to the chemical composition of the host semiconductor material.
- Option (d) describes a 'heterojunction' (e.g., GaAs and AlGaAs), which is the opposite of a homogeneous junction.
MES Jr. Grade • 2024 • Paper-I
The purpose of choke in a fluorescent tube is
A)
to decrease the current
B)
to increase the current
C)
to decrease the voltage momentarily
D)
to increase the voltage momentarily
A fluorescent tube requires a high starting voltage to ionize the gas inside the tube and initiate the discharge process, but it requires a much lower voltage to maintain the arc once it has started. The 'choke' (which is an inductor) serves two primary purposes:
1. **Starting (Voltage Spike):** When the starter switch opens, the magnetic field in the choke collapses rapidly. According to Lenz's Law, this creates a high-voltage inductive kick (voltage spike) that is sufficient to ionize the gas in the tube, effectively increasing the voltage momentarily to start the lamp.
2. **Ballasting (Current Limiting):** Once the tube is conducting, it behaves like a negative resistance device. The choke then acts as a ballast to limit the current to a safe operating level to prevent the tube from drawing excessive current and burning out.
Comparing the options:
- Option (a) describes the 'ballast' function during steady-state operation, but the primary 'purpose' of the choke in the context of starting the tube is the voltage spike.
- Option (b) is incorrect as the choke limits current, it doesn't increase it.
- Option (c) is incorrect as decreasing voltage would prevent the tube from starting.
- Option (d) correctly identifies the inductive action required to strike the arc.
MES Jr. Grade • 2024 • Paper-I
Which one is an integrating type measuring instrument?
A)
Ammeter
B)
Voltmeter
C)
Wattmeter
D)
watt-hour meter
Measuring instruments are broadly classified into two categories based on how they indicate the measured quantity: Indicating instruments and Integrating instruments.
1. **Indicating Instruments**: These instruments indicate the instantaneous value of the electrical quantity being measured at the moment of observation. Examples include Ammeters (measure current), Voltmeters (measure voltage), and Wattmeters (measure active power). These use a pointer and a scale to show the current value.
2. **Integrating Instruments**: These instruments measure the total amount of energy or quantity delivered over a specific period. They 'integrate' (sum up) the instantaneous values over time.
Analysis of options:
- **Ammeter (a)**: Indicates instantaneous current. (Indicating type)
- **Voltmeter (b)**: Indicates instantaneous voltage. (Indicating type)
- **Wattmeter (c)**: Indicates instantaneous power. (Indicating type)
- **Watt-hour meter (d)**: Measures the total electrical energy consumed over a period of time (Energy = Power × Time). It integrates the power over the time interval, making it an integrating instrument.
Therefore, the watt-hour meter is the correct answer.
MES Jr. Grade • 2024 • Paper-I
The driving point impedance function Z(s)= s/(s^2+1) can be realized as a
A)
R-C network
B)
R-L network
C)
L-C network
D)
R-L-C network
To determine the type of network that can realize the driving point impedance function Z(s) = s / (s^2 + 1), we analyze the properties of the function based on network synthesis theory:
1. **Analysis of the Function**: The given function is Z(s) = s / (s^2 + 1).
2. **Lossless Network Condition**: A network is lossless (consisting only of Inductors (L) and Capacitors (C)) if its driving point impedance Z(s) is a lossless function. A function is lossless if:
- It is a rational function of s.
- All its poles and zeros are simple and lie on the imaginary axis (jω axis).
- The poles and zeros alternate between the origin and infinity along the imaginary axis.
3. **Checking the Poles and Zeros**:
- **Zeros**: Set the numerator to zero: s = 0. There is a simple zero at the origin.
- **Poles**: Set the denominator to zero: s^2 + 1 = 0 => s = ±j1. There are simple poles on the imaginary axis at s = j and s = -j.
4. **Alternation Property**:
- Zero at s = 0
- Pole at s = ±j1
- (The next zero would be at infinity)
Since the poles and zeros are simple, lie on the imaginary axis, and alternate, Z(s) is a lossless function.
5. **Conclusion**: A lossless driving point impedance function can be realized using only L and C elements. If the function had real parts in the poles/zeros or coefficients that implied energy dissipation, it would require resistors (R). Since this function is purely imaginary for s = jω (Z(jω) = jω / (1 - ω^2)), it represents a purely reactive network.
Therefore, the network is an L-C network.
MES Jr. Grade • 2024 • Paper-I
Inductance is measured in terms of capacitance and resistance by using
A)
Schering bridge
B)
Anderson bridge
C)
Maxwell-Wien bridge
D)
Wien bridge
The question asks for a bridge used to measure inductance in terms of capacitance and resistance.
1. **Anderson Bridge**: This is a modification of the Maxwell-Wien bridge. It is specifically designed to measure self-inductance in terms of a standard capacitor (C) and resistors (R). It is highly accurate because it allows the use of a fixed capacitor and variable resistors to balance the bridge, making it the standard choice for measuring inductance using capacitance.
2. **Schering Bridge**: This bridge is primarily used for the measurement of capacitance and the dissipation factor (dielectric loss) of a capacitor, not for measuring inductance.
3. **Maxwell-Wien Bridge**: While this bridge measures inductance, it does so by comparing the unknown inductance with a known standard inductor (not primarily in terms of a capacitor) or using a capacitor in a way that is less precise for a wide range of values compared to the Anderson bridge. The Anderson bridge was developed specifically to improve upon the Maxwell-Wien bridge by allowing the use of a smaller, fixed capacitor.
4. **Wien Bridge**: This bridge is used for the measurement of frequency (often used in audio oscillators) and the measurement of capacitance/resistance in specific RC circuits, but not for measuring inductance.
MES Jr. Grade • 2024 • Paper-I
The superposition theorem is applied when the circuit contains
A)
a single voltage source
B)
a single current source
C)
a number of voltage or current sources
D)
a number of voltage sources only
The Superposition Theorem is a fundamental principle in network analysis used for linear circuits. It states that in a linear network containing multiple independent sources (voltage sources and/or current sources), the current through (or voltage across) any element is the algebraic sum of the currents (or voltages) produced by each source acting independently, while all other independent sources are replaced by their internal impedances.
- Option (a) and (b) are incorrect because if there is only a single source, the superposition theorem is not needed; simple Ohm's law or KVL/KCL suffices.
- Option (d) is incorrect because the theorem is not limited to voltage sources; it applies equally to current sources or a combination of both.
- Option (c) is correct because the theorem is specifically designed to simplify the analysis of circuits containing multiple (a number of) independent sources.
MES Jr. Grade • 2024 • Paper-I
If a dynamometer type wattmeter is connected in an AC circuit, the power indicated by the wattmeter will be
A)
volt-ampere product
B)
average power
C)
peak power
D)
instantaneous power
A dynamometer-type wattmeter consists of two coils: a fixed current coil (connected in series with the load) and a movable pressure coil (connected in parallel with the load). The torque produced in the instrument is proportional to the product of the current flowing through the current coil and the voltage across the pressure coil. In an AC circuit, the instantaneous torque varies sinusoidally; however, due to the inertia of the moving system, the pointer cannot follow these rapid fluctuations and instead settles at a position representing the time-average of the instantaneous power. Mathematically, the power indicated is P = Vrms * Irms * cos(φ), where cos(φ) is the power factor. This value is the 'average power' (also known as real power or active power).
Why other options are incorrect:
- (a) Volt-ampere product: This refers to Apparent Power (S = V * I), which is measured by a power analyzer or calculated, not by a standard wattmeter.
- (c) Peak power: This is the maximum instantaneous value of power, which the instrument's inertia filters out.
- (d) Instantaneous power: This varies 100/120 times per second in a 50/60Hz system; a mechanical pointer cannot track this.
MES Jr. Grade • 2024 • Paper-I
At what temperature does the resistivity of mercury completely disappear?
A)
4.2°K
B)
12.5°K
C)
22.2°K
D)
55.2°K
Superconductivity is a phenomenon where the electrical resistivity of a material drops to zero when cooled below a characteristic temperature known as the critical temperature (Tc). Mercury (Hg) was the first material in which superconductivity was discovered by Heike Kamerlingh Onnes in 1911. He observed that the resistivity of mercury completely disappeared at a critical temperature of approximately 4.15 K to 4.2 K.
Analysis of options:
- Option (a) 4.2°K: This is the scientifically accepted critical temperature for mercury.
- Option (b) 12.5°K: This does not correspond to the Tc of mercury.
- Option (c) 22.2°K: This does not correspond to the Tc of mercury.
- Option (d) 55.2°K: This is far above the critical temperature of mercury; mercury is a Type-I superconductor with a very low Tc.
MES Jr. Grade • 2024 • Paper-I
Resistance of a conductor is
A)
directly proportional to the conductivity of the conductor
B)
directly proportional to the resistivity of the conductor
C)
directly proportional to the cross sectional area of the conductor
D)
inversely proportional to the length of the conductor
The resistance (R) of a conductor is determined by its physical dimensions and the nature of the material it is made of. The fundamental formula for resistance is: R = ρ(L/A), where:
- R is the Resistance
- ρ (rho) is the Resistivity of the material
- L is the Length of the conductor
- A is the Cross-sectional area of the conductor.
Analyzing the options based on this formula:
1. Option (b) is correct because R is directly proportional to the resistivity (ρ). If the resistivity of the material increases, the resistance increases.
2. Option (a) is incorrect because conductivity (σ) is the reciprocal of resistivity (σ = 1/ρ). Therefore, resistance is inversely proportional to conductivity.
3. Option (c) is incorrect because resistance is inversely proportional to the cross-sectional area (A). A thicker wire has less resistance.
4. Option (d) is incorrect because resistance is directly proportional to the length (L). A longer wire has more resistance.
MES Jr. Grade • 2024 • Paper-I
A superconducting material when placed in a magnetic field will
A)
not influence the magnetic field
B)
repel all the magnetic lines of force passing through it
C)
attract the magnetic field towards its centre
D)
attract the magnetic field but transfer it into a concentrated zone
The phenomenon described in the question is known as the Meissner Effect. When a material transitions into the superconducting state (below its critical temperature Tc), it doesn't just become a perfect conductor; it becomes a perfect diamagnet. According to the Meissner Effect, a superconductor expels all magnetic flux from its interior. This is achieved by the spontaneous creation of surface currents that generate a magnetic field exactly equal and opposite to the applied external magnetic field, resulting in a net magnetic field of zero (B = 0) inside the bulk of the material. Therefore, the material repels all magnetic lines of force passing through it.
Analysis of other options:
- Option (a) is incorrect because the superconductor actively alters the field by expelling it.
- Option (c) is incorrect because attracting the field would imply paramagnetism or ferromagnetism, which is the opposite of the Meissner effect.
- Option (d) is incorrect because the field is expelled from the interior, not concentrated within it.
MES Jr. Grade • 2024 • Paper-I
Strain gauge LVDT and thermocouple may be classified as
A)
Active transducers
B)
Analogue transducers
C)
Primary transducers
D)
None of the above
To determine the correct classification, let's analyze the three devices mentioned:
1. **Strain Gauge**: It converts mechanical strain into a change in electrical resistance. The output is a continuous electrical signal (voltage/current) proportional to the strain.
2. **LVDT (Linear Variable Differential Transformer)**: It converts linear motion into a continuous AC voltage signal.
3. **Thermocouple**: It converts temperature differences into a continuous DC voltage (Seebeck effect).
Analysis of Options:
- **Active Transducers (Option a)**: An active transducer generates its own electrical output without an external power source (e.g., Thermocouple). However, a Strain Gauge and LVDT are **passive transducers** because they require an external excitation voltage to operate. Since not all three are active, this option is incorrect.
- **Analogue Transducers (Option b)**: All three devices produce a continuous output signal that varies linearly or proportionally with the input physical quantity. They do not produce discrete pulses or digital bits. Therefore, they are all classified as analogue transducers. This is the correct option.
- **Primary Transducers (Option c)**: A primary transducer is the first element in a measurement chain that senses the physical quantity. While a thermocouple is a primary transducer, an LVDT is often used as a secondary transducer (converting a displacement provided by another element into voltage). This classification is not universally applicable to all three in the same way 'analogue' is.
Conclusion: The common characteristic shared by the strain gauge, LVDT, and thermocouple is that they all provide an analogue output signal.
MES Jr. Grade • 2024 • Paper-I
The effect of doping intrinsic semiconductor is to
A)
move the Fermi level away from the centre of the forbidden band
B)
move the Fermi level towards the centre of the forbidden band
C)
change the crystal structure of the semiconductor
D)
keep the Fermi level at the middle of the forbidden band
1. **Intrinsic Semiconductors**: In a pure (intrinsic) semiconductor, the number of electrons in the conduction band equals the number of holes in the valence band. Consequently, the Fermi level (Ef), which represents the chemical potential of electrons, lies almost exactly in the middle of the forbidden energy gap (band gap).
2. **N-type Doping**: When a semiconductor is doped with pentavalent impurities (donors), the concentration of electrons increases. This introduces donor energy levels just below the conduction band, shifting the Fermi level upwards, moving it away from the center and closer to the conduction band.
3. **P-type Doping**: When doped with trivalent impurities (acceptors), the concentration of holes increases. This introduces acceptor energy levels just above the valence band, shifting the Fermi level downwards, moving it away from the center and closer to the valence band.
4. **Conclusion**: In both cases of doping (N-type or P-type), the Fermi level is displaced from its original central position in the forbidden band. Therefore, the effect of doping is to move the Fermi level away from the center of the forbidden band.
**Analysis of other options:**
- Option (b) is incorrect because the Fermi level is already at the center in an intrinsic state; doping moves it away, not towards it.
- Option (c) is incorrect because doping involves replacing a very small fraction of atoms; it changes the electrical properties, not the overall crystal structure (e.g., diamond cubic structure of Silicon remains).
- Option (d) is incorrect because keeping the Fermi level at the middle is the characteristic of an intrinsic semiconductor, not a doped one.
MES Jr. Grade • 2024 • Paper-I
An AC voltage of magnitude 20 V is applied to a circuit consisting of a resistor and an inductive coil with a negligible resistance. If the voltage across resistor is 12 V, the voltage across the coil is
A)
6V
B)
8V
C)
10V
D)
16V
1. Analysis of the Circuit: The circuit consists of a resistor (R) and an inductive coil with negligible resistance (pure inductor L) connected in series.
2. Phasor Relationship: In a series RL circuit, the voltage across the resistor (Vr) and the voltage across the inductor (Vl) are 90 degrees out of phase. The total applied voltage (Vs) is the phasor sum of these two voltages.
3. Mathematical Formula: The relationship is given by the Pythagorean theorem: Vs² = Vr² + Vl².
4. Given Values:
- Total applied voltage (Vs) = 20 V
- Voltage across resistor (Vr) = 12 V
5. Calculation:
Vl² = Vs² - Vr²
Vl² = (20)² - (12)²
Vl² = 400 - 144
Vl² = 256
Vl = √256 = 16 V.
6. Conclusion: The voltage across the coil is 16 V. Options a, b, and c are incorrect because they do not satisfy the phasor sum requirement for an RL circuit.
MES Jr. Grade • 2024 • Paper-I
Two identical coaxial coils carry the same current I but in opposite directions. The magnitude of the magnetic field B at a point on the axis midway between the coils is
A)
same as that produced by one coil
B)
twice that produced by one coil
C)
half that produced by one coil
D)
zero
1. **Understanding the Setup**: We have two identical coaxial coils. 'Identical' means they have the same radius (R) and the same number of turns (N). 'Coaxial' means they share the same central axis.
2. **Magnetic Field of a Single Coil**: The magnetic field B produced by a circular coil at a point on its axis is given by the formula B = (μ₀NI²R²) / [2(R² + x²)^(3/2)], where x is the distance from the center of the coil to the point of observation.
3. **Analyzing the Midpoint**: Let the distance between the two coils be 'd'. The point midway between the coils is at a distance x = d/2 from both coils. Since the coils are identical and carry the same current I, the magnitude of the magnetic field produced by each coil at this midpoint is exactly the same (B₁ = B₂).
4. **Direction of the Field**: The direction of the magnetic field is determined by the right-hand thumb rule. Because the currents flow in **opposite directions**, the magnetic field vectors produced by the two coils at the midpoint will point in opposite directions along the common axis.
5. **Superposition Principle**: The net magnetic field B_net is the vector sum of the individual fields: B_net = B₁ + B₂. Since the magnitudes are equal (B₁ = B₂) but the directions are opposite (B₁ = -B₂), the net field is B_net = B₁ - B₁ = 0.
6. **Conclusion**: The magnetic fields cancel each other out perfectly at the midpoint, resulting in a net magnetic field of zero.
MES Jr. Grade • 2024 • Paper-I
A wire conductor of resistance 1 Ω is doubled in length. Its resistance becomes
A)
the same as that when cold
B)
higher than cold resistance
C)
lower than cold resistance
D)
higher or lower than the cold resistance depending on the supply frequency
The resistance (R) of a conductor is governed by the formula R = ρ(L/A), where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
1. According to the formula, resistance is directly proportional to length (R ∝ L).
2. If the length of the wire is doubled (L becomes 2L), the resistance will also double (R becomes 2Ω), assuming the cross-sectional area and material remain constant.
3. Since 2 Ω is greater than the original 1 Ω (which represents the initial or 'cold' state of the wire), the resistance becomes higher.
Regarding the options:
- Option (a) is incorrect because resistance changes with length.
- Option (b) is correct because doubling the length increases the resistance.
- Option (c) is incorrect because resistance increases, not decreases, with length.
- Option (d) is incorrect because DC resistance of a wire is independent of supply frequency.
MES Jr. Grade • 2024 • Paper-I
How much electrical energy is consumed in operation of a 20 W bulb 5 hours per day in a month of 30 days?
A)
2kWh
B)
3kWh
C)
4kWh
D)
5kWh
To calculate the electrical energy consumed, we use the formula: Energy (E) = Power (P) × Time (t).
1. **Identify the given values:**
- Power (P) = 20 W
- Daily usage time = 5 hours/day
- Total days = 30 days
2. **Calculate total operating hours for the month:**
Total time (t) = 5 hours/day × 30 days = 150 hours
3. **Calculate total energy in Watt-hours (Wh):**
Energy = 20 W × 150 hours = 3,000 Wh
4. **Convert Watt-hours to kilowatt-hours (kWh):**
Since 1 kWh = 1,000 Wh,
Energy = 3,000 Wh / 1,000 = 3 kWh
Comparing this result to the options:
- Option (a) 2kWh is incorrect.
- Option (b) 3kWh is correct.
- Option (c) 4kWh is incorrect.
- Option (d) 5kWh is incorrect.
MES Jr. Grade • 2024 • Paper-I
Which statement is not applicable to the Coulomb’s law?
A)
The force between the two charged particles is along the line joining them.
B)
The force between them is directly proportional to the product of two charges.
C)
The force between them is directly proportional to the product of their masses.
D)
The force between them is inversely proportional to the square of the distance between them.
Coulomb's Law describes the electrostatic force between two point charges. The mathematical expression is F = k * (|q1 * q2|) / r², where F is the force, q1 and q2 are the magnitudes of the charges, r is the distance between them, and k is Coulomb's constant.
Analyzing the options:
- Option (a) is correct: The electrostatic force acts along the straight line connecting the centers of the two charges.
- Option (b) is correct: According to the formula, F ∝ q1 * q2.
- Option (c) is incorrect: Coulomb's Law deals with electric charges, not masses. The force proportional to the product of masses is Newton's Law of Universal Gravitation (F = G * m1 * m2 / r²), not Coulomb's Law.
- Option (d) is correct: According to the formula, F ∝ 1/r² (Inverse Square Law).
Since the question asks which statement is NOT applicable, option (c) is the correct answer.
MES Jr. Grade • 2024 • Paper-I
The phenomenon by which a material in an external magnetic field becomes magnetized and remain magnetized for that time period is called
A)
diamagnetism
B)
ferromagnetism
C)
paramagnetism
D)
ferrimagnetism
The question describes the ability of a material to become strongly magnetized in an external magnetic field and retain that magnetization (remanence) even after the external field is removed. This is the defining characteristic of ferromagnetism.
1. **Ferromagnetism (Option b):** Ferromagnetic materials (like iron, cobalt, and nickel) have 'domains' where atomic magnetic moments are aligned. An external field aligns these domains, and due to strong exchange interactions, they remain aligned even after the field is removed, resulting in permanent magnetization.
2. **Diamagnetism (Option a):** These materials create an induced magnetic field in the opposite direction to the applied field and lose all magnetization immediately when the field is removed.
3. **Paramagnetism (Option c):** These materials are weakly attracted to a magnetic field. While they magnetize in the presence of a field, the thermal agitation causes them to lose their magnetization almost instantly once the external field is removed.
4. **Ferrimagnetism (Option d):** While ferrimagnets also exhibit spontaneous magnetization and hysteresis (like ferromagnets), the term 'ferromagnetism' is the standard general answer for the phenomenon of becoming and remaining magnetized in basic engineering contexts, and ferromagnets typically exhibit the strongest version of this effect.
MES Jr. Grade • 2024 • Paper-I
On a B-H curve, initially B increases as H increases and gets saturation, after that as H decreases B decreases but does not follows the previous path. This phenomenon is called
A)
Harmonics
B)
Saturation
C)
Magnetization
D)
Hysteresis
The question describes the behavior of a ferromagnetic material when subjected to a varying magnetic field (H).
1. **Initial Magnetization**: As the magnetic field intensity (H) increases from zero, the magnetic flux density (B) increases until it reaches a point where all magnetic domains are aligned; this is called 'Saturation'.
2. **The Phenomenon**: When H is decreased back to zero, the magnetic flux density (B) does not return to zero along the same path it took during magnetization. Instead, it follows a different path, leaving behind some residual magnetism (Retentivity).
3. **Definition**: This 'lagging' of the magnetic flux density (B) behind the magnetic field intensity (H) is known as Hysteresis (derived from the Greek word 'hysteresis' meaning 'lagging behind').
Why other options are incorrect:
- **Harmonics**: These are sinusoidal components of a signal with frequencies that are integer multiples of the fundamental frequency; they are not a property of the B-H curve path.
- **Saturation**: This is the state where an increase in H no longer results in a significant increase in B. While mentioned in the question, it is a point on the curve, not the phenomenon of the path difference.
- **Magnetization**: This is the general process of inducing magnetic properties in a material, not the specific phenomenon of the non-reversible path.
MES Jr. Grade • 2024 • Paper-I
In ferro-electric material, as the applied electric field is gradually reduced to zero, the residual polarization is known as
A)
coercive polarization
B)
remanent polarization
C)
electronic polarization
D)
hysteresis polarization
In ferroelectric materials, the relationship between the applied electric field (E) and the resulting polarization (P) is characterized by a hysteresis loop. When an external electric field is applied, the dipoles align, increasing the polarization. As the applied electric field is gradually reduced back to zero, the material does not return to a zero-polarization state; instead, it retains a certain amount of polarization. This remaining polarization at zero field is termed 'remanent polarization' (or residual polarization).
Analysis of other options:
- a. Coercive polarization (or Coercive Field): This is the intensity of the reverse electric field required to reduce the polarization back to zero.
- c. Electronic polarization: This is a basic type of polarization occurring in all atoms where the electron cloud shifts relative to the nucleus; it is not specific to the hysteresis behavior of ferroelectrics.
- d. Hysteresis polarization: This is not a standard term for a specific value, but rather 'hysteresis' refers to the overall phenomenon/loop of the lag between the field and the polarization.