There is a horizontal cylindrical uniform but time-varying nagnetic field increasing at a constant rate `dB//dt` as shown in Fig. 3.173. A charged particle having charge `q` and mass `m` is kept in euilibrium, at the top of a spring of spring constant `K`, in such a way that it is on the horizontal line passing through the center of the magnetic field as shown in the figure. The compression in the spring will be

Options

A. `(1)/(K)[mg-(qR^(2))/(2l)(dB)/(dt)]`
B. `(1)/(K)[mg+(qR^(2))/(l)(dB)/(dt)]`
C. `(1)/(K)[mg+(2qR^(2))/(l)(dB)/(dt)]`
D. `(1)/(K)[mg+(qR^(2))/(2l)(dB)/(dt)]`

Answer

D

Explanation

`E2pil=piR^(2)((dB)/(dt))," "E=(R^(2))/(2l)((dB)/(dt))`
`qE+mg=Kx`
`x=(qR^(2))/(K2l)((dB)/(dt))+(mg)/(K),x=(1)/(K)[mg+(qR^(2))/(2l)(dB)/(dt)]`