First slide

Electric field

Question

A small element $Δ l$ is cut from a circular ring of radius R and $λ$ coulomb charge per unit length. The net electric field at the centre of ring is

Moderate

A

zero
B

$\frac{λ . Δ l}{4 π ε_{0} R^{2}}$
C

Infinity
D

$\frac{λ}{4 π ε_{0} . Δ l}$

Solution

Electric field due to ring at centre before the element is removed = 0
$E^{'} =$ electric field at the centre after the element is removed.
$E^{''} =$ electric field at the centre due to the element only $= \frac{λ . Δ l}{4 π ε_{0} R^{2}}$
Now, $\vec{E} = {\vec{E}}^{'} + {\vec{E}}^{''} \Rightarrow 0 = E^{'} + \frac{λ . Δ l}{4 π ε R^{2}}$
$∴ |E^{'}| = \frac{λ . Δ l}{4 π ε_{0} . R^{2}}$

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