Problem: A piece of wire is bent to form a circle with radius r. It has a steady current I flowing through it in a counterclockwise direction as seen from the top (looking in the negative z direction). (Figure 1)Part AWhat is Bz(0), the z component of B⃗  at the center (i.e., x = y = z = 0) of the loop?Express your answer in terms of I, r, and constants like μ0 and π.

FREE Expert Solution

Magnetic field due to the element of current, idl at the center of the loop is expressed as:

dB=μ04π(idl×RR3)

The vector R projects the element to center of the loop.

The magnitude of dB can be written as:

dB=μ04π(idl·R sin90°R3)=μ0idl4πR2

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Problem Details

A piece of wire is bent to form a circle with radius r. It has a steady current I flowing through it in a counterclockwise direction as seen from the top (looking in the negative direction). (Figure 1)

Part A

What is Bz(0), the z component of B⃗  at the center (i.e., = 0) of the loop?

Express your answer in terms of Ir, and constants like μ0 and π.