Why does a charged particle entering a uniform magnetic field at right angles follow a circular path?

The force is always perpendicular to the velocity and constant in magnitude, so it acts as a centripetal force that continually turns the particle without changing its speed.

Explain why a magnetic field does no work on a moving charge.

The force is always at right angles to the velocity, so there is no component of force along the motion and the kinetic energy cannot change.

Derive the expression for the radius of the circular path of a charged particle in a uniform magnetic field.

Setting the magnetic force equal to the centripetal force gives qvB = mv²/r, so r = mv/(qB).

OCR A-Level Physics B H557

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Charge and Field

Moving charges in magnetic fields

3 things to know
Components 01, 02 and 03

Overview

Recall questions on the force equation and its condition, its direction, why the path curves and no work is done, radius and period calculations, crossed fields, and particles spiralling towards the poles.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Write the equation for the force on a charged particle moving through a magnetic field, and state the condition for its use.

Key term

How is the direction of the magnetic force on a moving positive charge found?

Numbers

Calculate the force on an electron moving at 2.0 × 10⁶ m s⁻¹ at right angles to a field of flux density 0.30 T.

Questions from this subtopic

Each one with the model answer underneath.

1
Write the equation for the force on a charged particle moving through a magnetic field, and state the condition for its use.
Model answer
The force is F = qvB, and it applies when the velocity of the particle is at right angles to the magnetic field.
2
How is the direction of the magnetic force on a moving positive charge found?
Model answer
Fleming's left-hand rule is used with the second finger pointing along the direction of motion of the positive charge, and for a negative charge the force is in the opposite direction.
3
Why does a charged particle entering a uniform magnetic field at right angles follow a circular path?
Model answer
The force is always perpendicular to the velocity and constant in magnitude, so it acts as a centripetal force that continually turns the particle without changing its speed.
4
Explain why a magnetic field does no work on a moving charge.
Model answer
The force is always at right angles to the velocity, so there is no component of force along the motion and the kinetic energy cannot change.
5
Calculate the force on an electron moving at 2.0 × 10⁶ m s⁻¹ at right angles to a field of flux density 0.30 T.
Model answer
F = qvB = 1.60 × 10⁻¹⁹ × 2.0 × 10⁶ × 0.30 = 9.6 × 10⁻¹⁴ N.
6
Derive the expression for the radius of the circular path of a charged particle in a uniform magnetic field.
Model answer
Setting the magnetic force equal to the centripetal force gives qvB = mv²/r, so r = mv/(qB).

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