Question

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

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

Answer 1

Correct Answer - D
(d) `E2pil = pir^(2)((dB)/(dt)), E = (R^(2))/(2l)((dB)/(dt))`
`qE + mg = Kx`
`rarr` `x = (qR^(2))/(K2l)((dB)/(dt)) + (mg)/(K), x = (1)/(K)[(mg + (qR^(2))/(2l)(dB)/(dt)]`