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

1. Two metal plates are connected to a 9V battery with negligible internal resistance. If the plates are 10 cm apart, what is the electric field at either of the plates?

$E_{electric}=\frac{V_{electric}}{d}=\frac{9}{0.1}=90{\text{ Vm}}^{-1}$

2. What is the electric field at the midpoint between the plates?

The whole point of a uniform electric field is that the field does not change anywhere between the plates - at the midpoint, as anywhere, it is 90 NC⁻¹.

3. The charge on an electron is -1.6 x 10⁻¹⁹ C. What is the electric field 1μm from a hydrogen nucleus?

$E_{electric}=\frac{Q}{4\pi {ϵ}_0{r}^2}=\frac{1.6\times 10^{-19}}{4\pi \times 8.85\times 10^{-12}\times (10^{-6}{)}^2}=1440{\text{ Vm}}^{-1}$

4. What is the direction of this field?

The hydrogen nucleus has a positive charge, so the electric field goes away from the nucleus (by convention).

5. A 2C charge is placed 1m from a -1C charge. At what point will the electric field be 0?

Define the distance r as shown:

$\frac{2}{4\pi {ϵ}_0(1+r{)}^2}=\frac{1}{4\pi {ϵ}_0{r}^2}$

$\frac{2}{(1+r{)}^2}=\frac{1}{r^2}$

$\frac{(1+r{)}^2}{2}=r^2$

$(1+r{)}^2=2r^2$

$1+r=r\sqrt{2}$

$r(\sqrt{2}-1)=1$

$r=\frac{1}{\sqrt{2}-1}=\frac{\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)}=\sqrt{2}+1\approx 2.41\text{ m}$