A `U`-shaped wire of mass `m` and length `l` is immersed with its two ends in mercury (see figure). The wire is in a homogenous field of magnetic induction `B`. if a charge, that is, a current pulse `q=int idt`, set through the wire, the wire will jump up.

If the wire reaches height `h` calculate the magnitude of the charge or current pulse, assuming that the time of the current pulse is very small in comparision with the time of flight. Make use of the fact that impulse of force equals
`intFdt`, which equal `mv`. Evalute `q` for `B=0.1 Wb//m^(2), m=10 gm,l=20cm & h=3` meters.

Options

A. `sqrt(24)C`
B. `sqrt(48)C`
C. `sqrt(15)C`
D. None of these

Answer

C

Explanation

Mercury is a conductor so current can flow through mercury.
`F=ilB`
`intFdt=mv`
`intilBdt=msqrt(2gh)`
`q=intidt=(msqrt(2gh))/(lB)`
`=(10xx10^(-3)xxsqrt(2xx10xx3))/(20xx10^(-2)xx0.1)=sqrt(15)C`