Correct Answer - a
By exmining a small piece of the wire Fig. we find:
Dividing the rod into infinitiesimal sections of length dr.
The magnetic force on this section is `dF_1=IB dr` and is
perpendicular to the rod. The torque dt due to forceon this section
is `dtau=rdF_1=IBrdr`
The total torque is
`intdr=IBint_0^1r dr=1/2Il^2B=0.0442Nm^-1`,
clockwise. This is the same torque calculated from a force diagram
in which the total magnetic force `F_1 =ILB` acts at the centre of
the rod.
`F_1` produces a clockwise torque, so the spring force must produce
a couterclockwise torque. The spring force must be to left,
the spring is stretched:
axis at hinge, counterclockwise torque positive
`(kx)lsin 53^@-1/2Il^2B=0`
`x=(IlB)/(2ksin 53.0^@)=((6.50A)(0.200m)(0.340T))/(2(4.80Nm^-1) sin 53.0^@)`
`=0.05765m`