Two circular loops of wire, each containing a single turn, have the same radius

Question

Two circular loops of wire, each containing a single turn, have the same radius of 5.3 cm and a common center. The planes of the loops are perpendicular. Each carries a current of 1.4 A. what is the magnitude of the net magnetic field at the common center? 3.2656e-5 Two long, straight wires are separated by 0.12 m. The wires carry currents of 8.5 A in opposite directions, as the drawing indicates. (a) Find the magnitude of the net magnetic field at the point A. 4.54e-5 T (b) Find the magnitude of the net magnetic field at the point B. 0 T

Explanation / Answer

7.

Magnetic field at the center of a current carrying loop of radius r is given by;

B = µ0I/2r

So field due to the loop 1 is;

B1 = µ0I/2r

or, B1 = (1.256X10-6 T-m/A)(1.4 A)/2(0.053 m) ------ (as 5.3 cm = 5.3/100 = 0.053m)

or, B1 = 16.58X10-6 T

Fiel B2 due to the second loop would have same magitude as B1 as both loops have same radius and current.

But at the common center, the fields due to the two loops will be perpendicular to each other.

So magnitude of resultant magentic field at the center is,

B = [B12 + B22] = (2)B1   (as B1 = B2)

or B = 23.46X10-6 T at the common center.

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