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Magnetic field in a region is given by B...

Magnetic field in a region is given by `B=B_0xhatk`. Two loops each of side a is placed in the magnetic region in the xy-plane with one of its sides on x-axis. If `F_1` is the force on loop 1 and d`F_2` be the force on loop 2, then

A

`F_1=F_2=0`

B

`F_1gtF_2`

C

`F_2gtF_1`

D

`F_1=F_2\ne0`

Text Solution

Verified by Experts

The correct Answer is:
D
Force on the wires paralle to x-axis will be obtained by integration (as Bprox and x coordinates vary along these wires). But on a loop there are two such wires. Force of them wil be equal and opposite.
Forces on two wires parallel to y-axis can be obtaine ddirectly (without integration) as value of `B` is same along these wires. But theri values will be different (as x-coordinate and therefore `B` is diferent).
`F_(net)=/_\F` (on two wires)
`=Ia(/_\B)=Ia(B_0)(/_\x)`
`=IaB_0(a)=IB_0a^2`
this is indecent of x
`:. F_1=F_2=IBla^2=0`
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