Free Electromagnetism MCQs with Answers

1. The SI unit of magnetic flux density is the

• A. weber
• B. tesla
• C. henry
• D. gauss

Explanation: One tesla is one weber per square metre, so the tesla measures flux density while the weber measures the total flux. The tesla is a large unit: the Earth's field is only about 50 microtesla, while an MRI scanner reaches 1.5 T or more. The henry is the unit of inductance and the gauss is the old CGS unit, with 1 T equal to 10,000 gauss.

2. The force on a straight conductor of length L carrying current I in a magnetic field B is given by

• A. F equals BIL sin theta
• B. F equals BIL cos theta
• C. F equals BI over L
• D. F equals B over IL

Explanation: The sine factor means the force is maximum when the conductor is perpendicular to the field and zero when it lies along the field, since a current parallel to B feels no force at all. The direction is given by Fleming's left hand rule, at right angles to both the current and the field. This force is what turns an electric motor.

3. Fleming's left hand rule gives the direction of

• A. the induced current in a generator
• B. the force on a current carrying conductor in a magnetic field
• C. the magnetic field around a wire
• D. the induced emf

Explanation: With the first finger along the field and the second along the current, the thumb gives the motion or force, which is the motor rule. The right hand rule is the generator rule, giving the direction of an induced current. Remembering that left is for motors and right is for generators avoids most of the confusion here.

4. Magnetic flux through a surface is defined as

• A. B times A times cos theta, where theta is the angle between B and the normal to the surface
• B. B times A times sin theta
• C. B divided by A
• D. B times A only, whatever the orientation

Explanation: Flux counts the field lines threading the surface, so it is greatest when the field is perpendicular to the surface, meaning parallel to its normal, and zero when the field lies in the plane of the surface. Its unit is the weber. Every question on induction depends on tracking how this quantity changes with time.

5. A charged particle moving parallel to a magnetic field experiences a force of

• A. maximum magnitude
• B. zero
• C. half the maximum
• D. qvB

Explanation: The magnetic force is qvB sin theta, and sin 0 is zero, so a charge travelling along the field lines feels nothing at all. The force is maximum when the motion is perpendicular to the field, and it is then qvB. This angular dependence is why charged particles from the Sun spiral in along the Earth's field lines near the poles and produce aurorae.

6. A charged particle entering a uniform magnetic field at right angles to it follows

• A. a straight line
• B. a parabola
• C. a circular path
• D. a spiral of increasing radius

Explanation: The magnetic force is always perpendicular to the velocity, so it changes direction without changing speed, which is exactly the condition for uniform circular motion. Setting qvB equal to mv squared over r gives a radius of mv over qB, the relation on which the mass spectrometer and the cyclotron depend. A particle entering at an angle follows a helix instead.

7. The magnetic force on a moving charge does no work on it because the force is

• A. very small
• B. always perpendicular to the velocity
• C. always opposite to the velocity
• D. not a real force

Explanation: Work is the dot product of force and displacement, and a force at right angles to the motion contributes nothing, so the kinetic energy and speed of the particle never change. Only the direction of travel is altered. This is why a magnetic field can steer a particle beam but cannot accelerate it, which is the job of the electric field in an accelerator.

8. The magnetic field around a long straight current carrying wire consists of

• A. straight lines parallel to the wire
• B. concentric circles centred on the wire
• C. lines radiating outwards from the wire
• D. no field at all

Explanation: The right hand grip rule gives the sense of the circles: point the thumb along the conventional current and the curled fingers show the field direction. The strength falls off as one over the distance from the wire, not as one over the distance squared. Inside a long solenoid, by contrast, the field is nearly uniform and parallel to the axis.

9. Two parallel wires carrying currents in the same direction

• A. attract each other
• B. repel each other
• C. exert no force on each other
• D. twist about one another

Explanation: Each wire sits in the field of the other, and applying the left hand rule shows the forces to be inward when the currents are parallel, outward when they are antiparallel. So like currents attract, which is the opposite of the behaviour of like charges. This force is what defines the ampere.

10. The radius of the circular path of a charged particle in a magnetic field is given by

• A. r equals qB over mv
• B. r equals mv over qB
• C. r equals mvB over q
• D. r equals qvB

Explanation: Equating the magnetic force qvB to the required centripetal force mv squared over r and rearranging gives r equal to mv over qB. A heavier or faster particle therefore curves less, while a stronger field curves it more tightly. Because the radius depends on mass for a given charge and speed, this expression is the basis of the mass spectrometer.