Question

The plastic rod forms a quarter-circle of radius $R$ and has uniform charge density $+\lambda$. Find the electric field at the origin.
$k=\frac{1}{4\pi {ϵ}_0}$

• A. $\frac{k\lambda }{r}$
• B. $\frac{\sqrt{2}k\lambda }{r}$
• C. $\frac{2k\lambda }{r}$
• D. $\frac{\sqrt{3}k\lambda }{r}$

Answer 1

The correct option is B $\frac{\sqrt{2}k\lambda }{r}$

Radius $=R$

Charge density $=+\lambda$

$k=\frac{1}{4\pi {ϵ}_0}$

electric field at the origin,

$=q=R\lambda$

$k=9\times {10}^9$ or in this case just a constant.

$E=k{R}^2\int dqr$

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

$=\frac{\sqrt{2}k\lambda }{r}$