Question

A uniformly charged ring with radius $0.5\text{m}$ has $0.002\pi \text{m}$ gap. If the ring carries a charge of $+1\text{C}$, the electric field at the centre is

• A. $7.5\times {10}^7{\text{NC}}^{-1}$
• B. $7.2\times {10}^7{\text{NC}}^{-1}$
• C. $6.2\times {10}^7{\text{NC}}^{-1}$
• D. $6.5\times {10}^7{\text{NC}}^{-1}$

Answer 1

The correct option is B $7.2\times {10}^7{\text{NC}}^{-1}$

Due to symmetric charge distribution electric field will only be produced by the charge on the element opposite to the gap.

Charge on the element opposite to the gap is

$dq=\frac{Q}{2\pi r}\left(0.002\pi \right)$

$\Rightarrow dq=\frac{1}{2\pi \left(0.5\right)}\times \frac{2\pi }{1000}$

$\Rightarrow dq=2\times {10}^{-3}\text{C}$

Since, the gap is very small, it can be treated as a point charge.

Now, the electric field at the centre of the given ring is given by,

$E=\frac{Kdq}{r^2}$

Where, $K=9\times {10}^9$ and $r=0.5\text{m}$

Substituting above values, we get

$E=\frac{9\times {10}^9\times 2\times {10}^{-3}}{(0.5{)}^2}$

$\therefore E=7.2\times {10}^7{\text{NC}}^{-1}$

Hence, option (b) is correct answer.