Two coplanar and concentric circular loops of wire carry currents of I 1 = 6.30

Question

Two coplanar and concentric circular loops of wire carry currents of I1 = 6.30 A and I2 = 2.90 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? (answer in Two coplanar and concentric circular loops of wire carry currents of I1 = 6.30 A and I2 = 2.90 A in opposite directions as in the figure below. (Answer in

Two coplanar and concentric circular loops of wire carry currents of I1 = 6.30 A and I2 = 2.90 A in opposite directions as in the figure below. (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. (Answer in cm) r2 = ______cm (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? (answer in Two coplanar and concentric circular loops of wire carry currents of I1 = 6.30 A and I2 = 2.90 A in opposite directions as in the figure below. (Answer in µT)

Explanation / Answer

a)

The magnitude of the net magnetic field at the center of the two loops is given by

B =uoni1/2r1 -uoni2/r2

Here the number of turns are the same which isn=1

B =uon/2[i1/r1-i2/r2] =(4*3.14*10-7*1/2)[6.30/12 -2.90/8.50] =(4*3.14*10-7*1/2)[0.525 -0.341]=1.15*10-7T =0.115uT

b)

The magnitude of the net magnetic field at the center of the two loops is given by

B =uoni1/2r1 -uoni2/r2

0=(4*3.14*10-7*1/2)[6.30/12 -2.90/r2]

Now by solving we get r2 =18.212/3.297 =5.52cm

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