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Home » There are two current-carrying planar coils made each from identical wires of length L. C1 is circular and C2 is square. They are so constructed that they have the same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.
There are two current-carrying planar coils made each from identical wires of length L. C1 is circular and C2 is square. They are so constructed that they have the same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.
CBSE | Class 12 | Magnetism and Matter | ncert exemplar | Physics
There are two current-carrying planar coils made each from identical wires of length L. C1 is circular and C2 is square. They are so constructed that they have the same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.

The circular coil C1 has a radius of R, a length of L, and a number of turns per unit length of n1 = L/2R.

The square C2 has a side, a perimeter, and a number of turns per unit length of n2 = L/4a.

Magnetic moment of C1 = m1 = n1iA1

Magnetic moment of C2 = m2 = n2iA2

m1 = LiR/2

m2 = Lia/4

Moment of inertia of C1 = I1 = MR2/2

Moment of inertia of C2 = Ma2/12

Solving the above, we get, a = 3R

i

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