First slide

Electric field

Question

A ring of radius R has charge -Q distributed uniformly over it. Calculate the charge (q) that should be placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant 'R' from the centre of the ring. If the value of $q = \frac{Q}{4} \sqrt{Ω}$ . The value of $Ω$ is __________.

Moderate

Solution

Electric field at point P due to charge of ring is
$E = \frac{k Q x}{{(R^{2} + x^{2})}^{3 / 2}}$
$At x = R : E = \frac{k Q}{2 \sqrt{2} R^{2}} directed towards the centre.$
$Electric field at P due to centre charge: \frac{k q}{R^{2}}$
For net field to be zero at P:
$\frac{k q}{R^{2}} = \frac{k Q}{2 \sqrt{2} R^{2}} \Rightarrow q = \frac{Q}{2 \sqrt{2}} = \frac{Q}{4} \sqrt{2}$

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