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

e = 1.6 x 10⁻¹⁹C

1. A positron (charge +e) is 1 μm from a lithium nucleus (charge +3e). What is the magnitude of the force acting on each of the particles? In what direction is it acting?

$F_{electric}={\frac {kQq}{r^{2}}}={\frac {8.99\times 10^{9}\times 1\times 3\times (1.6\times 10^{-19})^{2}}{(10^{-6})^{2}}}=6.90\times 10^{-16}{\mbox{ N}}$

This may seem tiny, but the mass of an electron is also tiny, so the acceleration is considerable.

2. An electron is 1mm from the positively charged plate in a uniform electric field. The potential difference between the plates is 20V, and the plates are 10 cm apart. What force is acting on the electron? In what direction?

The 1mm is a red herring.

$F_{electric}={\frac {qV}{d}}={\frac {1.6\times 10^{-19}\times 20}{0.1}}=3.2\times 10^{-17}{\mbox{ N}}$

3. The acceleration due to gravity around a point mass is constant, irrespective of the mass of the objects it is acting on. The acceleration due to electricity around a point charge is not. Use Newton's Second Law (F=ma) to explain this.

$a={\frac {F}{m}}$

$a_{grav}={\frac {GMm}{mr^{2}}}={\frac {GM}{r^{2}}}$

$a_{electric}={\frac {kQq}{mr^{2}}}$

The m cancels for gravitational acceleration, but not for electrical acceleration, since charge does not provide a resistance to a force.

4. An insulator contains charged particles, even though the overall charge on the insulator is 0. Why is the insulator attracted by a nearby charge?

The electrons in the atoms can move within certain bounds. Being in an electric field means that they spend more time closer to a positive charge, and so the parts of the insulator which are attracted to the charge end up being closer to the charge than those which are repelled. This means that the attractive force on the insulator is greater than the repulsive force. This causes the insulator as a whole to be attracted to the charge if it is positive. If it is negative, the reverse happens, and the insulator is repelled.

5. Where in the charged conducting plates which create a uniform electric field would you expect to find the charge located? Why?

The charges are free to move within a conductor. The opposite charges in each plate are attracted to each other and try to move as close to each other as possible. So, they end up on the inside edge of the plates.