Two long coaxial solenoids of radius R and 2 R have equal number of turns per unit length. They carry time-varying currents i 1 = 2 k t and i 2 = k t respectively, in the same direction. A point charge released between the solenoids at a distance r , is seen to move along a circular path. Then the value of r is

Step-by-step solution

The magnetic field due to the inner solenoid (within its volume) is B 1 = μ 0 n 2 k t The magnetic field due to the outer solenoid (within its volume) is B 2 = μ 0 n k t The flux of magnetic field through the circular area of radius r is ϕ = B 1 π R 2 + B 2 π r 2 ⇒ ϕ = π μ 0 n k t 2 R 2 + r 2 If E → is the induced electric field at r , then ∮ E → . d r → = - d ϕ d t ⇒ E × 2 π r = π μ 0 n k 2 R 2 + r 2 ⇒ E = μ 0 n k R 2 r + r 2 The radius of the circle traversed by the charged particle is r = m v q B 2 v = E q t m =