Question

Half ring of radius r has a charge of lambda per unit length the electric field at the centre is

Answer 1

Answer:

Half ring of radius r has a charge of lambda per unit length the electric field at the centre is as in above attachment.

Answer 2

Given that,

Radius of half ring = r

A charge of lambda per unit length.

We need to calculate the charge

Using formula of charge

$Q=\lambda\times L$

Where, L = total length

Put the value of L

$Q=\lambda\times\pi R$

We need to calculate the electric field

Using formula of electric field

$E=\dfrac{kQ}{R^2}$

Where, k = constant

R = radius

Q = charge

Put the value of Q into the formula

$E=\dfrac{k\lambda\times\pi r}{r^2}$

$E=\dfrac{k\pi\lambda}{r}$

Hence, The electric field at the centre is $\dfrac{k\pi\lambda}{r}$.