Figure shows sqare current caarrying coil of edge lengthL. The magnetic field on the coil is given by `vec(B)=(B_(0)y)/L hat(i)+(B_(0)x)/L hat(j)` where `B_(0)` is a positive constant.

Options

A. If coil is free to rotate about x axis torque on the coil is given by `1/2iAB_(0)hat(i)`
B. If coil is free to rotate about y-axis torque on coil is given by `-1/2iAB_(0)hat(j)`
C. Resultant force on coil is zero.
D. Equation for the torque `vec(mu)xxvec(B)` where mu is magnetic moment of coil is not valid on the coil.

Answer

A, B, C, D

Explanation

Wire segment(1)

`(dvec(f))=underset0oversetLinti dx((B_(0)x)/2)=(iB_(0)L)/2`
`dvec(f)=(-B_(0)L)/2hat(k)`
Similary for `vec(f)_(2)=-(-iB_(0)L)/2hat(k)`
`vec(f)_(3)=(iB_(0)L)/2hat(k)`
`vec(f)_(4)=(iB_(0)L)/2 hat(k)`
`vec(f)_(n)=0`
If coil is constrained to rotate about
`y-ax is |vec(tau)|=1((B_(0)L)/2)L`
`=(iAB_(0))/2`
Rightarrow Similarly for torque about torque has same magnitude