Question

A circular loop of radius `R` is bent along a diameter and given a shape as shown in figure. One of `30, A` the se micircles (KNM) lies in the xz-plane and the other one (KLM) in the yz-plane with their centres at origin. Current I is flowing through each of the semicircles as shown in figure.

(a) A particle of charge q is released at the origin with a velocity `v =- v_0hati`. Find the instantaneous force `F` on the particle. Assume that space is gravity free.
(b) If an external uniform magnetic field `B_0hatj` is applied, determine the force `F_1` and `F_2` on the semicircles `KLM` and `KNM` due to the field and the net force `F` on the loop.

Answer 1

Correct Answer - A::B::D
a. `B` at origin `B_(KLM)=B_(KNM)`
`=(mu_0I)/(4R)(-hati+hatj)`
Now, we can apply `F=q(vxxB)` for finding force on it.
b. In uniform magnetic field,
`F_(KLM)=F_(KNM)=E_(KM)`
`=I(IxxB)`
`=I[(2R(-hatk)}xx{B_0hatj}]`
`=(2B_0IR)hati`
`:`. Net force is two times of the above value.