Question

A half ring of radius R has a charge of $\lambda$per unit length. The electric field at the centre is $\left( k = \frac{1}{4\pi\varepsilon_{0}} \right)$

• A. Zero
• B. $\frac{k\lambda}{R}$
• C. $\frac{2k\lambda}{R}$
• D. $\frac{k\pi\lambda}{R}$

Answer 1

Answer: (B)

$\frac{k\lambda}{R}$

Answer 2

According to question we can draw following figure.

As we have discussed earlier in theory $\theta = \frac{\pi}{3} + \alpha$

$\tan\alpha = \frac{1}{2}\tan\frac{\pi}{3}$⇒ $\alpha = \tan^{- 1}\frac{\sqrt{3}}{2}$

So, $\theta = \frac{\pi}{3} + \tan^{- 1}\frac{\sqrt{3}}{2}$