There are two current carrying planar coils made each from identical wires of length L. C1 is circular (radius R) and C2 is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find an in terms of R.
C1 is a circle of radius R 
Length wire used L1 = 2
C2 is a square of side a 
Length of wire used L2 = 4a
Total Length of the wire = L = L1 = L2
… (1)
Magnetic moment of C1 = m1 = n1iA1
Similarly,
Moment of Inertia of c1
Moment of Inertia of c2
Frequency of c1
Frequency of c2
By substituting the values
The value of a is 3R.
1