A conducting wire carrying an electric current I forms a closed circular loop of

Question

A conducting wire carrying an electric current I forms a closed circular loop of diameter d as shown in the figure

a. Derive the symbolic expression for the magnetic field at the center of the loop, in terms of the current, diameter, and appropriate physical constants.

Now, assume that the current and the diameter have the numerical values in the figure.

b. What is the direction of the magnetic field at the ceneter of the loop?

c. What is the magnitude of the magnetic field at the center of the loop?

Explanation / Answer

if r is the radius of the loop
a)
at the center

B = mue*I/(2*pi*r)

or B = mue*I/(pi*d) (here d---> diametr)

b) if current flows clockwise direction, direction of B is in to the page


if current flows counetr clockkwise direction,   direction of B is out of the page

c) substtitute mue = 4*pi*10^-7

I = ...A

d = ... m

and get B

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