Free Charged Particle in a Magnetic Field MCQs with Answers

1. 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.

2. 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.

3. 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.

4. 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.

5. In a mass spectrometer, ions of the same charge and speed but different masses are separated because

• A. heavier ions move faster
• B. heavier ions follow a path of larger radius in the magnetic field
• C. lighter ions are stopped by the field
• D. heavier ions lose their charge

Explanation: The radius mv over qB is proportional to mass when charge, speed and field are fixed, so heavier ions curve less sharply and strike the detector further along. Measuring where each beam lands therefore measures the mass. This is how isotopes were discovered and how their relative abundances are determined.