(a) force on a charged particle travelling at right angles to a uniform…

The idea

A charged particle moving at right angles to a uniform magnetic field experiences a magnetic force. The field is uniform, so B has the same magnitude and direction everywhere in the region. Because the velocity is perpendicular to B, the force magnitude is F = BQv, where B is flux density in tesla, Q is charge in coulomb and v is speed in m s⁻¹. The force is always perpendicular to both v and B, so it acts as a centripetal force and does no work: speed stays constant while direction changes. Example: an electron with Q = 1.6 × 10⁻¹⁹ C entering at 2.0 × 10⁶ m s⁻¹ through B = 0.50 T feels F = 0.50 × 1.6 × 10⁻¹⁹ × 2.0 × 10⁶ = 1.6 × 10⁻¹³ N.

What earns the marks

• States that the magnetic force acts only on a moving charge and is zero when v is parallel to B.
• Uses F = BQv for motion at right angles to a uniform magnetic field, with B in tesla, Q in coulomb and v in m s⁻¹.
• Recognises that the force is perpendicular to both v and B, so it changes direction of motion but not speed.
• Applies the equation to a numerical case, keeping charge magnitude and consistent SI units.

Common mistakes and how to put them right

• Using the full velocity vector in F = BQv when the motion is not at right angles.

  Put it right: The correct approach is to use only the component of velocity perpendicular to B, since the parallel component produces no force.

• Treating the magnetic force as doing work and changing the particle's kinetic energy.

  Put it right: The force is always perpendicular to velocity, so speed and kinetic energy remain constant.

• Substituting a negative charge value and expecting a negative force magnitude.

  Put it right: Q gives the magnitude of force while direction is found from the sign of the charge and the field geometry.

Exam tips

• Check the angle between v and B before choosing F = BQv; if the motion is not at right angles, use the perpendicular component of velocity.
• Convert all quantities to SI units, for example mT to T and cm to m, before substituting into the equation.
• Sketch the v and B directions and use the sign of the charge to decide the force direction, rather than relying on memory alone.