Questions: Magnetic Fields

Question 1

A proton enters a region of strong uniform magnetic field perpendicular to its velocity. Which of the following correctly describes what happens?

• A. The proton accelerates in the direction of the magnetic field lines
• B. The magnetic force changes the proton's direction but not its speed, causing it to curve in a circle
• C. The magnetic force does positive work on the proton, increasing its kinetic energy
• D. A proton moving slowly through the field experiences a stronger force than one moving quickly

Answer: (B)

The magnetic force F = qv × B is always perpendicular to the velocity. Since force is perpendicular to displacement (which is along v), the force does zero work and cannot change the particle's kinetic energy or speed. It only changes direction — the result is circular motion when B is uniform and perpendicular to v. Option C is the classic misconception: students often assume a strong field accelerates particles, but magnetic fields cannot change speed, only direction.

Question 2

A bar magnet is cut in half along the axis perpendicular to its length, separating the north and south poles. What do the two pieces become?

• A. One piece becomes a pure north magnetic monopole; the other becomes a pure south monopole
• B. Each piece becomes a complete dipole with its own north and south poles
• C. Both pieces lose all magnetism because the magnetic field depended on the charge separation
• D. One piece retains the full original field strength; the other has no field

Answer: (B)

There are no magnetic monopoles in classical electromagnetism. No matter how many times you cut a magnet, each piece develops its own north and south poles — the closed-loop topology of magnetic field lines is preserved at every scale. The misconception (that cutting separates the poles) reflects an analogy to positive and negative electric charges that simply does not apply to magnetism. Maxwell's equation ∇·B = 0 captures this: the divergence of B is always zero, meaning field lines never begin or end.

Question 3

Because the magnetic force on a moving charge is always perpendicular to the velocity, a magnetic field alone cannot increase or decrease a charged particle's kinetic energy.

• T. True
• F. False

Answer: True

Work equals force times displacement in the direction of force. Since the magnetic force is always perpendicular to the velocity (and hence to the displacement), no work is done — W = F·d = 0. Kinetic energy remains constant; only the direction of motion changes. This is why magnetic confinement in particle accelerators like cyclotrons can curve particle paths without speeding them up or slowing them down — a separate electric field is needed to actually accelerate the particles.

Question 4

Magnetic field lines behave like electric field lines: they originate on north poles and terminate on south poles.

• T. True
• F. False

Answer: False

Electric field lines begin on positive charges and end on negative charges — they have sources and sinks. Magnetic field lines form closed loops with no beginning or end: they emerge from one end of a magnet, arc around through the surrounding space, and re-enter through the other end, continuing through the magnet itself. There are no magnetic monopoles to serve as sources or sinks. This is captured by ∇·B = 0 (Gauss's law for magnetism), one of Maxwell's four equations.

Question 5

Why does a charged particle moving perpendicular to a uniform magnetic field travel in a circle? Explain the physical mechanism, not just the formula.

Model answer: The magnetic force on the particle is always perpendicular to its velocity. Perpendicular forces change direction but not speed — exactly the condition for circular motion. As the particle curves, its velocity direction changes, and the magnetic force direction changes with it, always staying perpendicular. This continuous redirection traces a perfect circle, with the magnetic force providing the centripetal acceleration. The radius depends on the particle's mass, charge, speed, and field strength — the particle essentially orbits in the magnetic field the way a satellite orbits a planet under gravity, except gravity does do work while the magnetic force does not.

The physical picture is: force perpendicular to velocity → direction changes → force direction updates to stay perpendicular → closed circular orbit. This is why cyclotrons can bend particle beams without changing their energy, and why the concept of 'magnetic confinement' in fusion reactors is possible.