Two coplanar and concentric circular loops of wire carry currents of I_1 = 6.50

Question

Two coplanar and concentric circular loops of wire carry currents of I_1 = 6.50 A and I_2 = 2.70 A in opposite directions as in the figure below. Let r_1 = 12.0 cm and r_2 = 8.90 cm. (a) What is the magnitude of the net magnetic field at the center of the two loops? (b) What is the direction of the net magnetic field at the center of the two loops? out of the page into the page toward the top of the page toward the bottom of the page (c) Let r_1 remain fixed at 12.0 cm and let r_2 be a variable. Determine the value of r_2 such that the net field at the center of the loops is zero.

Explanation / Answer

Here ,

a) for the net magnetic field at the of loop

magnetic field at the = -u0 * I1/(2r1) + u0 * I2/(2r2)

magnetic field at the = 4pi *10^-7 * ( -6.50/(2 * 0.12) + 2.70/(2 * 0.089) )

magnetic field at the = -1.50 *10^-5 T

the magnetic field at the is 1.50 *10^-5 T

b)

the direction of magnetic field is Into the page

c)

for the radius r2

4pi *10^-7 * ( -6.50/(2 * 0.12) + 2.70/(2 * r2) ) = 0

solving for r2

r2 = 4.98 cm

the radius r2 needed is 4.98 cm

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