Question

Which of the following graphs correctly represent the variation of electric field $E$ vs $r$ for a ring, where $r$ represents the distance from the centre of ring along its axis.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Electric field, $\overrightarrow{E}$ due to a ring of radius $R$ along its axis at distance $r$ from its centre is given by,

$|\overrightarrow{E}|=\frac{KQr}{(R^2+r^2{)}^{\frac{3}{2}}}$

At the centre of the ring, $r=0$ so, $|\overrightarrow{E}|=0$

At $r\to \infty$ we have,

$|\overrightarrow{E}|={lim}_{r\to \infty }\frac{KQr}{r^3{(\frac{R^2}{r^2}+1)}^{\frac{3}{2}}}=0$

Now, we know that,
$\overrightarrow{E}$ achieves its maxima at $r=\pm \frac{R}{\sqrt{2}}$

On plotting the above points we get the graph as shown below.


Hence, option (a) is correct answer.