Two coplanar and concentric circular loops of wire carry currents of I1 = 6.10 A

Question

Two coplanar and concentric circular loops of wire carry currents of I1 = 6.10 A and I2 = 2.70 A in opposite directions as in the figure below.

a) If r1 = 12.0 cm and r2 = 8.50 cm, what is the magnitude of the net magnetic field at the center of the two loops?
=____________ µT

(b) If r1 = 12.0 cm and r2 = 8.50 cm, what is the direction of the net magnetic field at the center of the two loops?

(c) Let r1 remain fixed at 12.0 cm and let r2 be a variable. Determine the value of r2 such that the net field at the center of the loop is zero.
r2 = _______________ cm

Please help, Thank You

Explanation / Answer

magnetic field at the centre due to a loop =i/2r where r is the radius of the circluar loop

a)magnetic field due to inner wire = (I2)/2r2 upwards

magnetic field due to outer wire= (I1)/2r1 downwards

hence net magnetic field = (I1)/(2r1)- (I2)/2(r2)

=/2 * ( 6.1/.12 - 2.7/.085) = 1.19 * 10^(-5) =11.9 micro tesla

since the value came out to be positive ,its direction is outside the plane of paper

b)magnetic field =/2 * ( 6.1/.12 - 2.7/.085)

outside the plane of paper

curl the fingers in the direction of current then the direction of thummb gives the direction of magnetic field.

c) (I1)/(2r1)- (I2)/2(r2)=0

hence r2=(I2)(r1)/(I1) = 2.7(12)/6.1 =5.31 cm

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