A-level Physics (Advancing Physics)/Electric Force

Electric fields are caused by charge. This charge can be either positive or negative. Like charges repel each other, and opposite charges attract each other. If we have two point charges of charge Q and q respectively, and they are a distance r apart, the force on each of them is:

$F_{electric}={\frac {kQq}{r^{2}}}={\frac {Qq}{4\pi \epsilon _{0}r^{2}}}$,

where k and ε₀ are constants (k = 8.99 x 10⁹ Nm²C⁻²,ε₀ = 8.85 x 10⁻¹²C²N⁻¹m⁻²). This means that, twice as far away from the point charge, the force on another charge decreases by a factor of 4. Electric force around a point charge is very similar to gravitational force around a point mass.

A uniform electric field consists of two conducting plates. These plates are oppositely charged, and infinitely wide. Obviously, infinitely wide conducting plates do not exist, so uniform electric fields do not exist. However, fields which approximate uniform electric fields do exist, provided we look towards the middle of the plates, and the plates are not too far apart - at the ends, the formulae for uniform fields no longer apply.

The force on a charge in a uniform electric field is given by:

$F_{electric}={\frac {qV}{d}}$,

where V is the potential difference between the two plates, q is the charge of the point charge upon which the force is acting, and d is the distance between the two plates. This force remains constant as the charge travels within the electric field.

Questions

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?

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?

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.

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?

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

Worked Solutions