Question

A thick shell with radius 2R has uniform density ρ c/m3. It has a spherical cavity of radius R as shownin the figure. A charge particle of mass m and charge Q is projected along the line AB at an angle θ in the cavity as shown. Select the correct statement (Assume particle doesn't comes out of cavity) : (A) Particle crosses line AB at a distance of          2 0 u sin 2 3m Q R from point A. (B) Average velocity of particle during the time it crosses line AB is greater than u cos . (C) Final speed when it crosses line AB is equal to initial speed. (D) It will move in a parabolic path in the cavity

Answer 1

Answer:

ANSWER

We can consider the electric field at center to be a sum of electric fields due to complete shell of charge density ρ if it did not have any cavity, and due to a sphere of cavity of charge density −ρ.

Due to symmetry, the electric at center due to former is zero.

The later produces an electric field at center towards right given as

E=

4πϵ

0

1

r

2

q

=

4πϵ

0

1

(2R)

2

ρ(

3

4

πR

3

)

=

12ϵ

0

ρR