A-level Physics (Advancing Physics)/Force/Worked Solutions

1. What force is exerted by a 1T magnetic field on an electron (of charge -1.6 x 10⁻¹⁹C) moving at 5% of the speed of light (3 x 10⁸ ms⁻¹)?

$F=Bqv=1\times -1.6\times 10^{-19}\times 0.05\times 3\times 10^{8}=2.4\times 10{-12}{\mbox{ N}}$

This may seem tiny, but remember that the acceleration of the electron will be far greater, as it has such a small mass. The fact that the electron was moving at 0.05c means that we don't have to do any relativistic corrections.

2. What force is exerted by a 5mT magnetic field on a 20 cm wire with resistance 1μΩ attached to a 9V battery?

$V=IR$

$I={\frac {V}{R}}$

$F=BIl={\frac {BVl}{R}}={\frac {5\times 10^{-3}\times 9\times 0.2}{10^{-6}}}=9{\mbox{ kN}}$

3. The following diagram shows a positive charge moving through a magnetic field. Draw an arrow representing the direction of the force on the charge.

Note that, if the charge had been negative, the force would be in the opposite direction (upwards).

4. The following diagram shows a wire in a magnetic field. Draw an arrow representing the direction of the force on the wire.