Question

For the given uniformly charged ring, which of the following curve of electric field $\left(E\right)$ versus distance from the centre of ring $\left(x\right)$ along $x-$ axis is correct?
[Consider only right side of ring]

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We know that, for a uniformly charged ring, the electric field along $x-$ axis

$E_x=\frac{kQr}{(r^2+R^2{)}^{3/2}}$

Here, in the graph, the distance from centre of the ring $\left(r\right)$ is taken along $x-$ axis.

$E_x=\frac{2\pi k\lambda Rr}{(r^2+R^2{)}^{3/2}}(\because \lambda =Q/2\pi R)$

for the given ring,
$\lambda ,R$ and $k$ are constant.

So, $2\pi k\lambda R=\text{constant}=\alpha \left(\text{let}\right)$

$\therefore E_x=\frac{\alpha x}{(x^2+R^2{)}^{3/2}}........\left(1\right)$

Now, from equation (1)

at $x=0\to E_x=0$

$x=\infty \to E_x=0$

$x=\frac{R}{\sqrt{2}}\to E_x=E_{\text{max}}$

Based on these observations and equation (1), option $\left(d\right)$ is correct.