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).

What is Bz (0), the z component of B 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.

Question

Physics

Micaela Burke

23 August, 14:54

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).

What is Bz (0), the z component of B 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.

+5

Answers (1)

Know the Answer?

Alma Keith · Answer 1

B=μ₀I/2r

Explanation:

Produced magnetic field due to an existing electric field through a coil or conductor can be explained by Biot-Savart Law. Formula for this law is:

dB = (μ₀I/4π. r²) dL

Here,

r=Radius of the loop

I and r are constants with respect to length L.

To convert linear displacement L into angular displacement Ф:

dL=r. dФ

So,

dB = (μ₀I/4π. r²) r. dФ

dB = (μ₀I/4π. r) dФ

Integrating both sides over the circle i. e. from 0 radians to 2π radians (360⁰), while the integration will apply only on dФ as all others are constants.

B = (μ₀I/4πr) (2π-0)

B = (μ₀I/2r)