Question

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop

(BL) to that at the centre of the coil (BC), i.e. R BL/BC will be
A. 1/N
B. N²
C. 1/N²
D. N

Answer 1

The ratio of the magnetic fields at the center of a single loop to a coil of N turns, when the same current is passed through both, is 1/N.

Step-by-step explanation:

The question asked is related to the magnetic fields created in two different configurations of a conducting wire when the same current is passed through both. When a single current-carrying wire is formed into a circular loop, the magnetic field at the center is given by the formula B = μ₁I/(2R), where R is the radius of the loop. For a circular coil with N identical turns, the magnetic field at the center is enhanced and is given by B = Nμ₁I/(2R).

This increase is due to the multiplicative effect of the N turns, each contributing to the total magnetic field at the center of the coil. If both wires have the same length and thus the same R when formed into loops, the magnetic field in the loop will be N times smaller than in the coil of N turns since the coil's magnetic field includes the factor of N. Therefore, the ratio of the magnetic fields at the center of the loop to the coil will be 1/N.