Two coplanar and concentric circular loops of wire carry currents of I_1 = 5.70

Question

Two coplanar and concentric circular loops of wire carry currents of I_1 = 5.70 A and I_2 = 2.50 A in opposite directions as in the figure below. If r_1 = 12.0 cm and r2 = 8.60 cm, what is the magnitude of the net magnetic field at the center of the two loops? I MT If r_1 = 12.0 cm and r_2 = 8.60 cm, 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 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 loop is zero

Explanation / Answer

here,
magnatic field in Circular loop is given as:

B = uo * I /2R
I1 = 5.70 A
I2 = 2.50 A

A.)
R1 = 12cm = 0.12m
R2 = 8.60cm = 0.086 m

Bnet = uo * I1 /2*R1 - uo * I2 /2*R2
Bnet = uo/2 (I1/R1 - I2/R2) -----------------------------(1)
Bnet = 12.56*10^-7 /2 (5.70/0.12 - 2.50/0.086)
Bnet = +1.16*10^-5 T

The magnitude of Net Magnatic Field Will be 1.16*10^-5 T

B.)
From A as magnatic Field is positive so it will be directed towards out of page.

C.)
R1 = 12cm = .12m
R2 = R2
Therefore Eqn 1 we get
Bnet = uo/2 (I1/R1 - I2/R2)
0 = uo/2 (5.70/0.12 - 2.50/R2)
5.70/0.12 = 2.50/R2

R2 = 0.052 m

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