5. A conductor wire consists of a circular loop of radius R = 10.0 cm and two st

Question

5. A conductor wire consists of a circular loop of radius R = 10.0 cm and two straight long sections as shown. The wire lies in the plane of the paper and carries a current I-40.0 A a) Find the magnetic field vector at the center of the loop b) We use another long straight wire that carries a current I. If we place this wire tangent to the loop on the opposite side of the first wire and parallel to it, what should be the value of I' and its direction, such that the magnetic filed at the center of the loop vanishes? c What is the force per unit length between the two straight wires?

Explanation / Answer

5)

a) at the center of the loop,

Bnet = B_wire + B_loop

= mue*I/(2*pi*R) + mue*I/(2*R)

= 4*pi*10^-7*40/(2*pi*0.1) + 4*pi*10^-7*40/(2*0.1)

= 3.31*10^-4 T

b) B_newwire = B_wire + B_loop

mue*I'/(2*pi*R) = 3.31*10^-4

I' = 3.31*10^-4*2*pi*R/mue

= 3.31*10^-4*2*pi*0.1/(4*pi*10^-7)

= 165.5 A

c) Force unit length between the two wires, F/L = mue*I*I'/(2*pi*2*R)

= 4*pi*10^-7*40*165.5/(2*pi*2*0.1)

= 6.62*10^-3 N/m

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