Hello, I need help solving PROBLEM B. please indicate all the steps in solving t

Question

Hello, I need help solving PROBLEM B. please indicate all the steps in solving this problem. Thank you!

Find the B-field (magnitude and direction) at point P due to the currents in the two wires Same problem as before, but now one current has been reversed. A 40-cm-diameter loop is made with 3 turns of wire, and 40 cm from its center a straight wire lies in the plane of the loop. You wind 200 turns of wire on an empty waxed paper tube over a length of 25 cm. What current must you supply to create a B-field in the middle of the solenoid equal to Earth s field?

Explanation / Answer

The idea here is that the B field from the top wire will be into the page and that of the bottom wire will be out of the page. They wire work againset each other.

For the top wire we get

B = oI/2r

B = (4 X 10-7)(3)/(2)(.22)

B = 2.73 X 10-6 T (into the page)

For the bottom wire

B = (4 X 10-7)(2)/(2)(.12)

B = 3.33 X 10-6 T (out the page)

The net will be out of the page, since the lower wire creates a larger B field. The magnitude is found by

3.33 X 10-6 - 2.73 X 10-6 = 6.06 X 10-7 T

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