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A rectangular loop with dimensions 4.20 cm by 9.50 cm carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 3.10×10−5 T and direction away from you as you view the plane of the loop. What are the magnitude and direction (clockwise or counterclockwise) of the current in the loop?

Answer :

Answer:

1.63 A and in clockwise direction

Explanation:

The magnetic field due to the rectangular loop is :

[tex]$B=\frac{2 \mu_0 I}{\pi}\left(\frac{\sqrt{L^2+W^2}}{LW}\right)$[/tex]

Given : W = 4.20 cm

                [tex]$=4.20 \times 10^{-2} \ m$[/tex]

            L = 9.50 cm

               [tex]$= 9.50 \times 10^{-2} \ m$[/tex]

            [tex]$B = 3.40 \times 10^{-5} \ T $[/tex]

   Rearranging the above equation, we get

[tex]$I=\frac{B \pi LW}{2 \mu_0\sqrt{L^2+W^2}}$[/tex]

[tex]$I=\frac{(3.40 \times 10^{-5}) \pi(9.50 \times 10^{-2})(4.20 \times 10^{-2})}{2(4 \pi \times 10^{-7})\sqrt{(9.50 \times 10^{-2})^2+(4.20 \times 10^{-2})^2}}$[/tex]

I = 1.63 A

So the magnitude of the current in the rectangular loop is 1.63 A.

And the direction of current is clockwise.

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