A particle of mass m and charge +q approaches from a very large distance towards a uniformly charged ring of radius R and charge, mass same as that of particle, with initial velocity v 0 along the a

Question

A particle of mass m and charge +q approaches from a very large distance towards a uniformly charged ring of radius R and charge, mass same as that of particle, with initial velocity $v_{0}$ along the axis of the ring as shown in the figure. What is the closest distance of approach between the ring and the particle? Assume the space to be gravity free and frictionless.

TestHub · Accepted Answer

mv 0 ​ = 2 mv ​ ∴ v = v 0 ​ /2 ​ 2 1 ​ m v 0 2 ​ = 4 π ε 0 ​ R 2 + x 2 ​ q 2 ​ + 2 ⋅ 2 1 ​ m ⋅ 4 v 0 2 ​ ​ ​ ⇒ 4 1 ​ m v 0 2 ​ = 4 π ε 0 ​ R 2 + x 2 ​ q 2 ​ ​ ⇒ x = π 2 ε 0 2 ​ m 2 v 0 4 ​ q 4 ​ − R 2 ​ ​

Physics - Electrostatics Question with Solution | TestHub

Options:

Doubts & Discussion