Question

An electron is moving in a circular orbit of radius r with an angular acceleration α. at the centre of the orbit is kept a conducting loop of radius r, (r << r). the emf induced in the smaller loop due to the motion of the electron is

Answer 1

it is given, that charge on electron = e

angular acceleration = α

as current = charge /time taken

so, current through complete oscillation, I = total charge/time period

= e/T

we know, T = 2π/ω

so, I = eω/2π ......(1)

now magnetic field at centre , B = μ0I/2R

= μ0eω/4πR [ from equation (1)]

magnetic flux, Φ = B.A = μ0eω/4πR × ( πr² )

= μ0eωr²/4R

induced emf = - dΦ/dt

= -d(μ0eωr²/4R)/dt

= - μ0er²/4R × dω/dt

=- μ0er²α/4R

hence, induced emf is - μ0er²α/4R