Question

Find electric field at point A, B, C, D due to infinitely long uniformly charged wire with linear charge density λ and kept along z-axis (as shown in figure). Assume that all the parameters are in S.l. units.

Answer 1

• Electric field at point A: $\vec{E}_A = \frac{\lambda}{2\pi\epsilon_0 r} \hat{i}$

• Electric field at point B: $\vec{E}_B = \frac{\lambda}{2\pi\epsilon_0 r} \hat{j}$

• Electric field at point C: $\vec{E}_C = -\frac{\lambda}{2\pi\epsilon_0 r} \hat{i}$

• Electric field at point D: $\vec{E}_D = -\frac{\lambda}{2\pi\epsilon_0 r} \hat{j}$

Answer 2

The electric field due to an infinitely long uniformly charged wire with linear charge density $\lambda$ at a perpendicular distance $r$ from the wire is given by:

$E = \frac{\lambda}{2\pi\epsilon_0 r}$

The direction of the electric field is radially outward from the wire if $\lambda$ is positive, and radially inward if $\lambda$ is negative.

Since points A, B, C, and D are located at the same perpendicular distance 'r' from the z-axis, the magnitude of the electric field at each of these points will be the same:

$E_{magnitude} = \frac{\lambda}{2\pi\epsilon_0 r}$

The directions at each point are as follows:

1. Point A: Located on the positive x-axis. The electric field is directed along the positive x-axis ($\hat{i}$).

2. Point B: Located on the positive y-axis. The electric field is directed along the positive y-axis ($\hat{j}$).

3. Point C: Located on the negative x-axis. The electric field is directed along the negative x-axis ($-\hat{i}$).

4. Point D: Located on the negative y-axis. The electric field is directed along the negative y-axis ($-\hat{j}$).