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Two concentric, circular wire loops with radii [tex]r_1 = 21.5 \, \text{cm}[/tex] and [tex]r_2 = 39.3 \, \text{cm}[/tex] carry clockwise currents of [tex]9.59 \, \text{A}[/tex] each. What is the magnetic field at the center of the loops?

Answer :

The magnetic field at the center of two concentric circular wire loops is found by calculating the magnetic field for each loop separately using Ampere's law and adding them together, as the currents are in the same direction.

The question involves finding the magnetic field at the center of two concentric, circular wire loops carrying clockwise currents. We use Ampere's law and the formula for the magnetic field (B) at the center of a single loop, B = (uI)/(2R), where u is the permeability of free space (u0 = 4π x 10-7 T·m/A), I is the current, and R is the radius of the loop. With both loops having the same currents but different radii, their respective magnetic fields at the center add up because the currents are in the same direction.

The magnetic field at the center due to the first loop (radius r1 = 0.215 m) carrying a current of 9.59 A is B1 = (u0 * 9.59 A) / (2 * 0.215 m). Similarly, we calculate B2 for the second loop (radius r2 = 0.393 m). The net magnetic field at the center is the sum of B1 and B2 since the currents are in the same direction.

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