Question

Consider two identical loops of currents aligned on the z axis. One loop is centered at (0,0,-2) and the other loop is centered at (0,0,2). Each loop has a radius of 4 m and carries a current of 2 A in the a, direction. Compute the z-component of the magnetic field along the z-axis (x-y-0) at the following locations: z=-2, -1, 0, 1,2 m. Put the results in a table for Hz vs z. Do not integrate using the Biot-Savart Law but use the result for the magnetic field of a loop of current on the z- axis from Example 7.3 of the textbook. What do you notice about the magnetic field between the two loops?

Answer 1

The student's question involves calculating the z-component of the magnetic field along the z-axis produced by two current-carrying loops. This setup resembles a Helmholtz coil arrangement, with the expectation that the magnetic field will be near zero between the loops and increase as one moves towards either loop.

Step-by-step explanation:

The student is asking for the computation of the z-component of the magnetic field along the z-axis produced by two identical current-carrying loops using a known result rather than direct integration with the Biot-Savart Law. The problem is equivalent to what is seen in a Helmholtz coil configuration, and the student is asked to calculate the magnetic field at different points on the z-axis between the two loops.

Without performing calculations, we can discuss qualitatively based on the principles outlined in the reference material. At the cente

r between the two loops (z = 0), the magnetic fields due to each loop will be equal in magnitude but opposite in direction, leading to a net magnetic field of zero. As we move away from the center towards one of the loops, the magnetic field due to that loop will increase in strength, while the influence of the other loop diminishes, resulting in a non-zero net magnetic field.