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 `vecB` is along `hatz,Fprop(L+R)`
B. If `vecB` is along `hatx,F=0`
C. If `vecB` is along `haty,Fprop(L+R)`
D. If `vecB` is along `hatz,F=0`

Answer

A,B,C

Explanation

`vecF=i(veclxxvecB)=i{2(L+R)hatixxvecB}`
If `vecB` is along `vecz`
`vecF=[i 2(L+R)B](-hatj)`
if `vecB` is along `hatx`
`vecF=0`
If This along `haty`
`vecF=i{2(L+R)B)hatk}`
`dvecF=i(vec(dl)xxvecB)`
In uniform magnetic field
`intdvecF=inti(dveclxxvecB)=i(intdveclxxvecB)`
`rArr vecF=i(vec(PQ)xxvecB)`
`(A) F=[i 2(L+R)B]=2iB(L+R)`
`(B) F=0`
`(C) F=[i2(L+R)B]=2iB(L+R)`
`(D)F=[i2(L+R)B]=2iB(L+R)`