Question

For the given uniformly charged quarter ring, the angle $\theta$ made by the net electric field at the centre with negative x-axis is equal to

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

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

Given that,
Charge per unit length $=\lambda$
Radius of the ring $=R$

We know that, for uniformly charged quarter ring, the electric fields along x-axis is given by, $E_x=\frac{k\lambda }{R}$
Electric field along y-axis, $E_y=\frac{k\lambda }{R}$
So, $\tan \theta =\frac{E_y}{E_x}=1$
$\Rightarrow \theta ={45}^{\circ }$
Hence, option (b) is correct.