A conductor wire consists of a circular loop of radius R = 20.0 cm and two strai

Question

A conductor wire consists of a circular loop of radius R = 20.0 cm and two straight long sections as shown. The wire lies in the plane of the paper and carries a current 1 = 160.0 A. A second conductor wire is shown in the same plane which carries a current I' at a distance of d = 12 cm from the center at some angle as shown. The I and I' current carrying wires are insulated from one another. What is the magnetic field vector at the center of the loop due to L. What should be the value and direction of I', such that the magnetic field at the center of the loop vanishes?

Explanation / Answer

a) We can think of the total magnetic field as the superposition of the field due to the long straight wire (having magnitude µ0I/2R directed out of the page) and the field due to the circular loop (having magnitude µ0I/2R and directed out of the page). The resultant magnetic field is

B = (µ0I/2R)[1+(1/)]

=> B = 6.63*10-4 T

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b)

µ0I'/2d = 6.63*10-4

=> I' = 397.8 A

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