Question

A charged particle of mass m, charge q moves with a speed vin a circular path of radius r around a long uniformly charged conductor having density X. Then​

Answer 1

Consider a Gaussian cynlinder of radius r and length l. Using Gauss's law the electric field at distance r is E.(2πrl)=

ϵ

0

λl

⇒E=

2πϵ

0

r

λ

Here the electrostatic force is equal to centrifugal force. i.e,

qE=

r

mv

2

q

2πϵ

0

r

λ

=

r

mv

2

orv

2

=

2πϵ

0

m

qλ

so v is independent of r.