Question

A rigid circular loop of radius r and mass m lies the x-y plane on a flat table and has a current i flowing in it. At this particular place, magnetic field is b=bxi =byj

Answer 1

N.B.: Your question is incomplete.

This should be like this,

A rigid circular loop of radius r and mass m lies the x-y plane on a flat table and has a current I flowing in it. At this particular place, magnetic field is b=bxi =byj. Derive the value of current I

Answer:

I = $mg/\pi r\sqrt{Bx^2+By^2}$

Explanation:

The radius of the circular loop is r. The mass of the loop is m.

Now the rigid circular loop lies on the x-y plane on a flat table. The current I is flowing in it.

At this particular place, magnetic field is B=bxi =byj

So, the net torque on the loop is

ζ= -Mbxi+Mbyj = Iπr²$\sqrt{Bx^2+By^2 }$   ------- (Equation 1)

By the torque balance equation we get ζ= mgr  ------- (Equation 2)

By equating the (Equation 1) and (Equation 2) we can say,

=> mgr= Iπr²$\sqrt{Bx^2+By^2 }$

=> I = $mg/\pi r\sqrt{Bx^2+By^2}$

Answer 2

So answer is = Mg/πr(Bx^2 + By^2)