In the figure, there are three infinitely long thin sheets having surface charge density + 3σ, -2σ$ and $+σ$ respectively. Determine magnitude and direction of the electric field at point A.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{σ}{ε_0}$ towards left
For an infinite sheet with surface charge density $\sigma$, the electric field on either side is
$E = \frac{\sigma}{2 \, \epsilon_0}$
Direction: away from the sheet if $\sigma$ is positive, towards the sheet if $\sigma$ is negative.
At point A (to the left of all sheets):
From $+3\sigma$ sheet: $E_1 = \frac{3\sigma}{2 \, \epsilon_0}$ towards left
From $-2\sigma$ sheet: $E_2 = \frac{2\sigma}{2 \, \epsilon_0} = \frac{\sigma}{\epsilon_0}$ towards right
From $+\sigma$ sheet: $E_3 = \frac{\sigma}{2 \, \epsilon_0}$ towards left
Net field at A:
$E_{\text{net}} = -\frac{3\sigma}{2 \, \epsilon_0} + \frac{\sigma}{\epsilon_0} - \frac{\sigma}{2 \, \epsilon_0}$
$E_{\text{net}} = -\frac{\sigma}{\epsilon_0}$
Therefore, the electric field at A is $\frac{\sigma}{\epsilon_0}$ towards left.