Moving charges in a magnetic field

Q1. A charged particle moves through a uniform magnetic field with its velocity perpendicular to the field. Which of the following correctly gives the magnitude of the magnetic force acting on it?

Multiple Choice · 1 point

• · F = BQv
• · F = BQ/v
• · F = Bv/Q
• · F = B²Qv

Q2. A proton moves to the right through a magnetic field directed into the page. Using Fleming's left-hand rule, in which direction does the magnetic force act on the proton?

Multiple Choice · 1 point

• · Downward
• · Upward
• · Into the page
• · To the left

Q3. An electron travels in the same direction and through the same magnetic field as the proton in the previous question. Compared to the proton, the force on the electron acts:

Multiple Choice · 1 point

• · In the same direction but with greater magnitude
• · In the same direction but with smaller magnitude
• · In the opposite direction with the same magnitude
• · In the opposite direction with greater magnitude

Q4. A particle with charge Q moves at speed v at an angle of 90° to a uniform magnetic field of flux density B. What happens to the magnetic force on the particle if its speed is halved?

Multiple Choice · 1 point

• · It remains the same
• · It doubles
• · It halves
• · It reduces to one quarter

Q5. A charged particle moves parallel to a uniform magnetic field. What is the magnetic force acting on it?

Multiple Choice · 1 point

• · Maximum, equal to BQv
• · Half the maximum force
• · Zero, since sin 0° = 0
• · Dependent on the sign of the charge

Q6. Why does a magnetic force on a moving charged particle do no work on it?

Multiple Choice · 1 point

• · The force is always parallel to the velocity
• · The force is always perpendicular to the velocity, so it has no component along the displacement
• · The particle has no mass so no kinetic energy can be transferred
• · The particle is decelerated and then re-accelerated, so net work is zero

Q7. A current-carrying wire experiences a force when placed in a magnetic field. Which of the following best explains why individual free electrons in the wire also experience a force?

Multiple Choice · 1 point

• · The electrons are stationary, so the force arises from their charge alone
• · The electrons are moving charges in the magnetic field, so each experiences F = BQv
• · The wire acts as a permanent magnet that repels the external field
• · The force on the wire is shared equally between the nuclei and electrons

Q8. A proton enters a region of uniform magnetic field directed out of the page and moves in a horizontal circle. In which direction does it orbit when viewed from above?

Multiple Choice · 1 point

• · Clockwise
• · Anticlockwise
• · It spirals inward
• · It travels in a straight line

Q9. A charged particle of mass m, charge Q, and speed v moves in a circle of radius r in a uniform magnetic field B. Which expression correctly gives the radius of the circular path?

Multiple Choice · 1 point

• · r = BQ/mv
• · r = mv/BQ
• · r = BQv/m
• · r = m/BQv

Q10. A proton and an alpha particle enter the same uniform magnetic field with the same speed. The charge of an alpha particle is 2e and its mass is approximately 4 times that of a proton. What is the ratio of the radius of the alpha particle's path to that of the proton?

Multiple Choice · 1 point

• · 1:1
• · 2:1
• · 4:1
• · 1:2

Q11. In a cyclotron, a particle is accelerated by an electric field each time it crosses the gap between the two D-shaped electrodes (dees). Which of the following correctly explains why the particle's orbital radius increases with each half-cycle?

Multiple Choice · 1 point

• · The magnetic field strength increases with each half-cycle
• · The particle gains kinetic energy and therefore speed, so r = mv/BQ increases
• · The charge on the particle increases with each crossing
• · The dees widen outward, forcing a larger radius

Q12. In a cyclotron, why does the time taken for one complete orbit remain approximately constant even as the particle speeds up?

Multiple Choice · 1 point

• · The electric field adjusts to compensate for the increasing speed
• · As speed increases, the radius decreases proportionally, keeping the period fixed
• · As speed increases, the orbital radius also increases proportionally, so the period T = 2πm/BQ is independent of speed
• · The particle slows down between accelerations so the average speed stays constant

Q13. In a velocity selector, a charged particle travels in a straight line. What condition must be satisfied for this to occur?

Multiple Choice · 1 point

• · The electric force and magnetic force act in the same direction and are both zero
• · The electric force equals the magnetic force in magnitude and they act in opposite directions
• · The electric field is parallel to the magnetic field
• · The particle must have a specific charge-to-mass ratio regardless of speed

Q14. In a velocity selector with electric field strength E and magnetic flux density B, a particle passes straight through undeflected. Which expression gives its speed?

Multiple Choice · 1 point

• · v = BE
• · v = B/E
• · v = E/B
• · v = E²/B

Q15. Put the following stages of a proton's journey through a cyclotron in the correct order.

Ordering · 5 points

• 1. Proton is released at the centre of the cyclotron with a small initial speed
• 2. Electric field in the gap accelerates the proton, increasing its kinetic energy
• 3. Proton travels in a semicircular path inside a dee under the influence of the magnetic field
• 4. Proton re-enters the gap, is accelerated again, and moves into a larger semicircle
• 5. Proton reaches the outer edge and is deflected out of the cyclotron as a beam

Q16. An electron (charge 1.6 × 10⁻¹⁹ C) travels at 3.0 × 10⁶ m/s perpendicular to a uniform magnetic field of flux density 0.25 T. What is the magnitude of the magnetic force acting on the electron?

Multiple Choice · 1 point

• · 7.5 × 10⁻¹⁴ N
• · 1.2 × 10⁻¹³ N
• · 4.8 × 10⁻¹⁴ N
• · 3.0 × 10⁻¹³ N

Q17. A proton (mass 1.67 × 10⁻²⁷ kg, charge 1.6 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m/s perpendicular to a magnetic field of flux density 0.40 T. What is the radius of the circular path it follows?

Multiple Choice · 1 point

• · 0.021 m
• · 0.52 m
• · 0.052 m
• · 0.104 m

Q18. A velocity selector has a uniform electric field of 4.8 × 10⁴ V/m and a perpendicular magnetic field of 0.12 T. What is the speed of a charged particle that passes through undeflected?

Multiple Choice · 1 point

• · 5.76 × 10³ m/s
• · 4.0 × 10⁵ m/s
• · 4.0 × 10⁶ m/s
• · 2.4 × 10⁵ m/s