Four very long, current-carrying wires in the same plane intersect to form a squ

Question

Four very long, current-carrying wires in the same plane intersect to form a square with side lengths of 45.0cm , as shown in the figure (Figure 1) . The currents running through the wires are 8.0 A, 20.0 A, 10.0 A, and I.

Find the magnitude of the current I that will make the magnetic field at the center of the square equal to zero.

What is the direction of the current I?

Four very long, current-carrying wires in the same plane intersect to form a square with side lengths of 45.0cm , as shown in the figure (Figure 1) . The currents running through the wires are 8.0 A, 20.0 A, 10.0 A, and I. Find the magnitude of the current I that will make the magnetic field at the center of the square equal to zero. What is the direction of the current I?

Explanation / Answer

B field is prop to current. The currents that create B fieldinto the page are

       10.0 + 8.0 =   18.0   amps

And the current that creates B field out of the pageis   20.0 amps

So you need   2.0 amps more creating B field intothe page. So

    I is   2.0 amps    and itis in DOWNWARD direction

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