Question

For the given uniformly charged quarter ring, net electric field at the center is

• A. $140\text{N/C}$
• B. $160\text{N/C}$
• C. $180\text{N/C}$
• D. $200\text{N/C}$

Answer 1

The correct option is C $180\text{N/C}$

Given:
$\lambda =+40\text{nC/m}=40\times {10}^{-9}\text{C}$
$R=2\sqrt{2}\text{m}$

We know that, for uniformly charged arc, net electric field is given by, $E=\frac{2k\lambda }{R}\sin \frac{\alpha }{2}$

For quarter ring, $\alpha ={90}^{\circ }$$E_{net}=\frac{\sqrt{2}k\lambda }{R}$
$\Rightarrow E_{net}=\frac{\sqrt{2}\times 9\times {10}^9\times 40\times {10}^{-9}}{2\sqrt{2}}$
$\Rightarrow E_{net}=180\text{N/C}$