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entric and lie in the same plane. The inner coil contains 120 turns of wire, has a rac carries a current of 6.0 A. The outer coil contains 130 turns and has a radius of 0.023 m. What must be tude of the current in the outer coil, such that the net magnetic field at the common center of the two c ber

entric and lie in the same plane. The inner coil contains 120 turns of wire, has a rac carries a current of 6.0 A. The outer coil contains 130 turns and has a radius of 0.023 m. What must be tude of the current in the outer coil, such that the net magnetic field at the common center of the two c ber

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Question:** Two circular coils are concentric and lie in the same plane. The inner coil contains 120 turns of wire, has a radius of 0.015 m, and carries a current of 6.0 A. The outer coil contains 130 turns and has a radius of 0.023 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero? **Answer:** To find the required current in the outer coil to ensure the net magnetic field at the center is zero, consider the following: 1. Calculate the magnetic field due to the inner coil using the formula for the magnetic field at the center of a circular loop: \[ B = \frac{\mu_0 \cdot n \cdot I}{2 \cdot r} \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)), \( n \) is the number of turns, \( I \) is the current, and \( r \) is the radius. 2. Use the same formula to calculate the magnetic field for the outer coil, but solve for the current \( I \) such that the magnetic fields cancel each other out. By setting the net magnetic field to be zero, you can solve for the unknown current in the outer coil.
Transcribed Image Text:**Question:** Two circular coils are concentric and lie in the same plane. The inner coil contains 120 turns of wire, has a radius of 0.015 m, and carries a current of 6.0 A. The outer coil contains 130 turns and has a radius of 0.023 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero? **Answer:** To find the required current in the outer coil to ensure the net magnetic field at the center is zero, consider the following: 1. Calculate the magnetic field due to the inner coil using the formula for the magnetic field at the center of a circular loop: \[ B = \frac{\mu_0 \cdot n \cdot I}{2 \cdot r} \] where \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)), \( n \) is the number of turns, \( I \) is the current, and \( r \) is the radius. 2. Use the same formula to calculate the magnetic field for the outer coil, but solve for the current \( I \) such that the magnetic fields cancel each other out. By setting the net magnetic field to be zero, you can solve for the unknown current in the outer coil.
Expert Solution
Step 1: Given and Required

Number of turns in the inner coil,

                                      N subscript 1 space equals space 120 space t u r n s

Radius of inner coil,

                                        R subscript 1 space equals space 0.015 space m

Current carried by inner coil,

                                         I subscript 1 space equals space 6.0 space A

Number of turns in the outer coil,

                                       N subscript 2 space equals space 130 space t u r n s

The radius of the outer coil,

                                       R subscript 2 space equals space 0.023 space m

We need to find the current in outer coil.

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