The closed loop shown in figure carries current I in the counterclockwise direct

Question

The closed loop shown in figure carries current I in the counterclockwise direction. The radious of the outher arc is b and that of inner arc is a.

(a) Find the magnetic field at point P

(b) Now we place this loop in an external magnetic field B that is perpendicular to the plane of the loop and into the page. What is the magnetic force acting on the loop from the external field B.

The closed loop shown in figure carries current I in the counterclockwise direction. The radious of the outher arc is b and that of inner arc is a. (a) Find the magnetic field at point P (b) Now we place this loop in an external magnetic field B that is perpendicular to the plane of the loop and into the page. What is the magnetic force acting on the loop from the external field B.

Explanation / Answer

a)
Bnet = B1 - B2

= (60/360)*mue*I/(2*a) - (60/360)*mue*I/(2*b)

= (mue*I/12)*(1/a - 1/b) (in to the page)

b)
Fnet = Fb - Fa

= B*I*Lb - B*I*La

= B*I*(60/360)*(2*pi*b) - B*I*(60/360)*(2*pi*a)

= (B*I*pi/6)*(b-a) ( to wards point P)

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