J. A straight conductor wire loops around in a complete circle of radius R secti

Question

J. A straight conductor wire loops around in a complete circle of radius R sections, as shown. This wire lies in the plane of the paper an 20.0 cm, between its two straight long d carries a current l = 60.0 A. A second straight n in the same plane which carries a current I' located a distance d-12 cm from the loop center, at some angle, as shown. The I and I' current carrying wires are insulated from one another. a) What is the magnetic field vector at the center of the loop due toI What should be the value and direction of I', such that the magnetic field at the center of the loop vanishes? b)

Explanation / Answer

a) magnetic field due to loop,

B1= µ0*I / 2R into the screen

magnetic field due to straight wire section

B2= µ0*I / 2*3.14*R into the screen

net field,

B=B1+B2

B=  µ0*I / 2R*(1+ 1/3.14)

B=2.689*10-4 T into the screen

b) The direction of I' should be from right to left so that the field due to it would be coming out of the screen and cancels the above field

field due to this wire,

B'= µ0*I' / 2*3.14*d

for the fields to cancel out their magnitudes should be equal and directions, opposite

B'=B

µ0*I' / 2*3.14*d =2.689*10-4

I'=161.34 Amp

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