Question

Two infinite sheets having equal charge densities $\sigma$ are placed in two perpendicular planes whose two-dimensional view is shown in the figure. The charges are distributed uniformly on sheets in electrostatic equilibrium condition. $E_1$ and $E_2$ are electric field at point $\text{P}$ due to the sheets $1$ and $2$ respectively and $E$ is the net electric field. The angle $\theta$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Electric field at point $\text{P}$ due to sheet $1$,

$E_1=\frac{\sigma }{2{ϵ}_0}$

Similarly, due to sheet $2$,

$E_2=\frac{\sigma }{2{ϵ}_0}$

Now, $\tan \theta =\frac{E_2}{E_1}$

$\Rightarrow \tan \theta =\frac{\frac{\sigma }{2{ϵ}_0}}{\frac{\sigma }{2{ϵ}_0}}=1$

$\Rightarrow \theta ={45}^{\circ }$

So, option $\left(b\right)$ is correct.