Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 26 cm and a current of 12 A. The bigger loop has a current of 20 A. The magnetic field at the center of the loops is found to be zero. Wo = 126 x 10-T m/A) Part A What is the radius of the bigger loop? Express your answer with the appropriate units. h RE Value Units Submit Request Answer

Answer 1

Sol::
Given:

Radius of smaller loop(Rs)= 2.6 cm
Current in smaller loop(Is)= 12 A
Current in bigger loop(Ib)=20 A
uo=1.26*10^-6 T.m/A

The magnetic field at the center of a circular loop of radius "r" and current "i" is;

B = ui/2r

The field is along the axis , one way for counterclockwise current and the other direction for clockwise current.

So, let us assume the current in the large loop is in the opposite direction and the set its field equal to the field of the small loop;

u(Ib)/2Rb = u(Is)/2*Rs

Rb = Rs*Ib/Is

= (2.6)(20)/(12)
= 4.33 cm
≈ 0.0433 m

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