A conductor (shown in the figure) carrying constant current `I` is kept in the `x-y` plane in a uniform magnetic field ` vec(B)`. If ` vec(F)` is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are)

Options

A. if B is along `hatz, F prop (L+R)`
B. if B is along `hatx,F=0`
C. if B is along `haty,F prop (L+R)`
D. if B is along `hatz,F=0`

Answer

A, B, C

Explanation

Force on the complete wire = force on straight wire PQ carrying a current I.
`F=I(PQxxB)=I[{2(L+R)hatixxB]`
This force is zero if B is along `hati` direction or x-direction. If magnetic field is along `hatj` direction of `hatk` direction,
`|F|=F(I)(2)(L+R)B sin 90^(@)` or `F=2I(L+R)B` or `F prop (L+R)`