Question

The electric field inside a capacitor is shown on the left in Figure 15.50. Which option (1–5) best represents the electric field at location A?

Short answer

Option (3) $E=0$ best represents the electric field at location A.

Step-by-step solution

Given data

A capacitor is provided.

Electric field of an infinite sheet

Electric field from infinite sheet of charge of charge density $\mathit{\sigma }$ is

role="math" localid="1668497576587" $\overrightarrow{\mathbf{E}}\mathbf{=}\frac{\mathbf{\sigma }}{\mathbf{2}{\mathbf{\epsilon }}_{\mathbf{0}}}\mathbf{(}\mathbf{\pm }\hat{\mathbf{n}}\mathbf{)}$

Here, ${\mathit{\epsilon }}_{\mathbf{0}}$ is the permittivity of free space and $\hat{\mathbf{n}}$ is the unit vector perpendicular to the sheet. The plus sign is for a positive charge distribution and the negative sign is for a negative charge distribution.

Determination of the field outside a capacitor

A capacitor consists of positively charged plate and a negatively charged plate kept close together parallel to each other. For fields measured close to the plates, the plates behave like infinite sheets. Thus from the above equation, the net field at point A is

$$\begin{gathered} \overrightarrow{E}=\frac{\sigma }{2{\epsilon }_0}\hat{n}-\frac{\sigma }{2{\epsilon }_0}\hat{n} \\ =0 \end{gathered}$$

Thus, option (3) best represents the field at location A.