The circular current loop of radius b shown in Fig. is mounted rigidly on the axle, midway between the two supporting cords. In the absence of an external magnetic field, the tensions in the cords are equal and are `T_0.`
a. What will be the tensions in the two cords when the vertical magnetic field B is present?
b. Repeat if the field is parallel to the axis.

Explanation

Let mass of hte hanging system is m, then
`2T_0=mg to` in the absence of magnetic field
(a) When magnetic field is applied:
`tau_0=MB=pib^2IB....(i)`
`T_1+T_2=mg...(ii)`
Taking torque about O:
`tau_0+T_2L/2=T_1L/2....(iii)`
Solve equations (i), (ii) and (iii) to get
`T_1=(mg)/2+(pib^2BI)/L and T_2=(mg)/2-(pib^2BI)/L`
(b) In this case, magnetic field will produce no torque, so tension
will remain same, `T_0=mg//2`