Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. If the frequency of the AC source is increased, what happens to the capacitive reactance?
A.Increases
B.Decreases
C.Remains the same
D.Becomes infinite
Solution
Capacitive reactance (X_C) is given by X_C = 1/(2πfC). If the frequency (f) increases, X_C decreases.
Correct Answer: B — Decreases
Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
A.1 kHz
B.10 kHz
C.100 Hz
D.1000 Hz
Solution
Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.
Correct Answer: A — 1 kHz
Q. A charged particle moves in a magnetic field. What is the condition for the particle to experience no magnetic force?
A.The particle must be at rest
B.The particle must be moving parallel to the magnetic field
C.The particle must be moving perpendicular to the magnetic field
D.The magnetic field must be zero
Solution
The magnetic force on a charged particle is given by F = q(v × B). If the velocity vector v is parallel to the magnetic field B, the cross product is zero, resulting in no magnetic force.
Correct Answer: B — The particle must be moving parallel to the magnetic field
Q. A charged particle moves in a magnetic field. What is the condition for the particle to experience maximum force?
A.Velocity is zero
B.Velocity is parallel to the field
C.Velocity is perpendicular to the field
D.Charge is zero
Solution
The magnetic force on a charged particle is given by F = qvB sin(θ). The force is maximum when the angle θ is 90 degrees, meaning the velocity is perpendicular to the magnetic field.
Correct Answer: C — Velocity is perpendicular to the field
Q. A charged particle moves in a magnetic field. What is the effect of the magnetic field on the particle's speed?
A.Increases speed
B.Decreases speed
C.No effect on speed
D.Reverses speed
Solution
The magnetic field exerts a force perpendicular to the velocity of the charged particle, which does not change its speed but alters its direction.
Correct Answer: C — No effect on speed
Q. A charged particle moves in a magnetic field. What is the effect of the magnetic field on the particle's motion?
A.It accelerates the particle
B.It changes the particle's speed
C.It changes the particle's direction
D.It has no effect
Solution
A magnetic field exerts a force on a charged particle that is perpendicular to both the velocity of the particle and the magnetic field, changing its direction but not its speed.
Correct Answer: C — It changes the particle's direction
Q. A charged particle moves in a magnetic field. What is the nature of the force acting on it?
A.Always in the direction of motion
B.Always opposite to the direction of motion
C.Perpendicular to the direction of motion
D.Depends on the charge of the particle
Solution
The magnetic force on a charged particle moving in a magnetic field is given by the Lorentz force law, which states that the force is perpendicular to both the velocity of the particle and the magnetic field.
Correct Answer: C — Perpendicular to the direction of motion
Q. A charged particle moves in a magnetic field. What path does it follow?
A.Straight line
B.Circular path
C.Elliptical path
D.Parabolic path
Solution
A charged particle moving in a magnetic field experiences a force perpendicular to its velocity, resulting in circular motion.
Correct Answer: B — Circular path
Q. A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop?
A.μ₀I/(2R)
B.μ₀I/R
C.μ₀I/(4R)
D.μ₀I/(8R)
Solution
The magnetic field at the center of a circular loop carrying current I is given by the formula B = (μ₀I)/(2R), where μ₀ is the permeability of free space.
Correct Answer: B — μ₀I/R
Q. A circular loop of wire carries a current. What is the direction of the magnetic field at the center of the loop?
A.Out of the plane
B.Into the plane
C.Clockwise
D.Counterclockwise
Solution
Using the right-hand rule, the magnetic field at the center of a current-carrying circular loop is directed out of the plane of the loop.
Correct Answer: A — Out of the plane
Q. A circular loop of wire is placed in a uniform magnetic field. If the magnetic field is increased, what happens to the induced EMF in the loop?
A.Increases
B.Decreases
C.Remains constant
D.Becomes zero
Solution
According to Faraday's law of electromagnetic induction, an increase in magnetic field through the loop induces an EMF in the loop.
Correct Answer: A — Increases
Q. A circular loop of wire is placed in a uniform magnetic field. What happens to the induced EMF if the area of the loop is increased?
A.Increases
B.Decreases
C.Remains the same
D.Depends on the magnetic field strength
Solution
According to Faraday's law of electromagnetic induction, the induced EMF is proportional to the rate of change of magnetic flux. Increasing the area increases the flux, thus increasing the induced EMF.
Correct Answer: A — Increases
Q. A circular loop of wire is placed in a uniform magnetic field. What happens to the induced EMF if the magnetic field strength is doubled?
A.Induced EMF is halved
B.Induced EMF remains the same
C.Induced EMF is doubled
D.Induced EMF is quadrupled
Solution
According to Faraday's law of electromagnetic induction, the induced EMF is directly proportional to the rate of change of magnetic flux. If the magnetic field strength is doubled, the induced EMF will also double.
Correct Answer: C — Induced EMF is doubled
Q. A coil of wire is placed in a changing magnetic field. What phenomenon is observed?
A.Electromagnetic induction
B.Magnetic resonance
C.Electrolysis
D.Thermal conduction
Solution
According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electromotive force (EMF) in the coil.
Correct Answer: A — Electromagnetic induction
Q. A coil of wire is placed in a magnetic field. If the magnetic field strength is doubled, what happens to the induced EMF?
A.It doubles
B.It remains the same
C.It halves
D.It quadruples
Solution
Doubling the magnetic field strength will double the induced EMF, as it is directly proportional to the magnetic field strength.
Correct Answer: A — It doubles
Q. A coil with 100 turns is placed in a magnetic field that changes at a rate of 0.5 T/s. What is the induced EMF in the coil?
A.50 V
B.100 V
C.200 V
D.25 V
Solution
Using Faraday's law, EMF = -N * (dΦ/dt) = -100 * 0.5 = -50 V. The induced EMF is 50 V.
Correct Answer: B — 100 V
Q. A coil with 100 turns is placed in a magnetic field that changes from 0.5 T to 1.5 T in 2 seconds. What is the induced EMF?
A.50 V
B.100 V
C.200 V
D.400 V
Solution
Induced EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5)/2) = -100 * (1/2) = -50 V. The magnitude is 50 V.
Correct Answer: B — 100 V
Q. A loop of wire is moved into a magnetic field at a constant speed. What happens to the induced EMF as it enters the field?
A.It increases
B.It decreases
C.It remains constant
D.It becomes zero
Solution
As the loop enters the magnetic field, the rate of change of magnetic flux increases, leading to an increase in induced EMF.
Correct Answer: A — It increases
Q. A loop of wire is moved into a uniform magnetic field at a constant speed. What happens to the induced EMF as it enters the field?
A.It increases
B.It decreases
C.It remains constant
D.It becomes zero
Solution
As the loop enters the magnetic field, the area exposed to the magnetic field increases, leading to an increase in the induced EMF.
Correct Answer: A — It increases
Q. A loop of wire is placed in a changing magnetic field. What phenomenon is this an example of?
A.Electromagnetic induction
B.Magnetic resonance
C.Electrostatics
D.Magnetic hysteresis
Solution
This is an example of electromagnetic induction, where a changing magnetic field induces an electromotive force (EMF) in the loop of wire.
Correct Answer: A — Electromagnetic induction
Q. A loop of wire is placed in a uniform magnetic field. If the field strength is increased, what happens to the induced EMF?
A.It increases
B.It decreases
C.It remains constant
D.It becomes zero
Solution
According to Faraday's law, an increase in magnetic field strength leads to an increase in the induced EMF.
Correct Answer: A — It increases
Q. A loop of wire is placed in a uniform magnetic field. What happens to the induced EMF if the area of the loop is increased?
A.Increases
B.Decreases
C.Remains the same
D.Depends on the magnetic field strength
Solution
According to Faraday's law of electromagnetic induction, the induced EMF is directly proportional to the rate of change of magnetic flux, which increases with an increase in the area of the loop.
Correct Answer: A — Increases
Q. A particle with charge q moves with velocity v in a magnetic field B. What is the expression for the magnetic force acting on the particle?
A.F = qvB
B.F = qvB sin(θ)
C.F = qB
D.F = qvB cos(θ)
Solution
The magnetic force acting on a charged particle moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity vector and the magnetic field vector.
Correct Answer: B — F = qvB sin(θ)
Q. A proton moves in a magnetic field and experiences a force. If the velocity of the proton is doubled, what happens to the magnetic force?
A.It doubles
B.It halves
C.It remains the same
D.It quadruples
Solution
The magnetic force is proportional to the velocity of the charge, so if the velocity is doubled, the magnetic force also doubles.
Correct Answer: A — It doubles
Q. A solenoid produces a magnetic field when an electric current passes through it. What happens to the magnetic field if the current is reversed?
A.The magnetic field disappears
B.The magnetic field direction reverses
C.The magnetic field strength increases
D.The magnetic field strength decreases
Solution
Reversing the current in a solenoid reverses the direction of the magnetic field according to the right-hand rule.
Correct Answer: B — The magnetic field direction reverses
Q. A solenoid produces a uniform magnetic field inside it. What factors affect the strength of this magnetic field?
A.Length of the solenoid
B.Number of turns per unit length
C.Current through the solenoid
D.All of the above
Solution
The strength of the magnetic field inside a solenoid is affected by the number of turns per unit length and the current flowing through it, as well as the length of the solenoid.
Correct Answer: D — All of the above
Q. A solenoid produces a uniform magnetic field inside it. What happens to the magnetic field strength if the current through the solenoid is doubled?
A.It remains the same
B.It doubles
C.It quadruples
D.It halves
Solution
The magnetic field strength inside a solenoid is directly proportional to the current flowing through it.
Correct Answer: B — It doubles
Q. A transformer works on the principle of:
A.Electromagnetic induction
B.Electrostatics
C.Magnetic resonance
D.Thermal conduction
Solution
A transformer operates on the principle of electromagnetic induction, transferring energy between coils through a changing magnetic field.
Correct Answer: A — Electromagnetic induction
Q. According to Ampere's Law, the line integral of the magnetic field B around a closed path is equal to what?
A.Zero
B.The product of permeability and current
C.The product of permittivity and charge
D.The electric field times the area
Solution
Ampere's Law states that the line integral of the magnetic field B around a closed path is equal to μ₀ times the total current I enclosed by the path.
Correct Answer: B — The product of permeability and current
Q. According to Ampere's Law, what is the magnetic field inside a long straight conductor carrying current I?
A.Zero
B.μ₀I/2πr
C.μ₀I/4πr
D.μ₀I/πr
Solution
Inside a long straight conductor, the magnetic field is zero because the contributions from all parts of the conductor cancel out.
