Question

A simple pendulum of length l and bob mass m is hanging in front of a large nonconducting sheet having surfacecharge density sigma.If suddenly a charge +q is given to the bob and it is released from the static position. Find maximum angle through which the string is deflected

Answer 1

Please see the attached picture to understand the question,

We can take the answer for this by applying F = ma to the bob vertical and horizontal directions,

Since the bob is not moving and it is balanced by the forces,when we apply the equation vertically, we will get,

TCos∅ = mg -----------------(1)

And Horizontally,

TSin∅ = Eq ------------------(2) ,  E - Electric Field Density of the Sheet

by (2)/(1),

Tan∅ = Eq/mg

We can Replace E by σ/ε where ε is the permittivity of a vaccum and it is a constant,

Then we can write,

Tan∅ = σq/εmg

Then,

∅ = Tan Inverse (σq/εmg)