You have two single turn circular loops of wire oriented such that they have a c

Question

You have two single turn circular loops of wire oriented such that they have a common center and the planes of the loops are perpendicular. As shown in the figure below, loop #1 lies in the in the xy-plane and has a counterclockwise current when viewed from the positive z-axis, while loop #2 lies in the xz-plane and has a counterclockwise current when viewed from the positive y-axis.

#1 1 #2 (a) If the loops each have a radius of 2.8 cm and they each carry a current of 1.3 A, determine the magnitude of the net magnetic field at the common center. (b) The direction of a vector in three dimensions is often given by the angle it makes with the positive x, y, and z-axes. What is the angle between the net magnetic field at the center and the positive x-axis? What is the angle between the net magnetic field at the center and the positive y-axis? What is the angle between the net magnetic field at the center and the positive z-axis?

Explanation / Answer

Here ,

magnetic field due to i1 and i2 are equal in magnitude

B1 = u0*I/(2R)

B = 4pi*10^-7 * 1.3/(2 * 0.028)

B = 2.92 *10^-5 T

now , net magnetic field , as these fields are perpendicular to each other

B = sqrt(2.92^2 + 2.92^2) *10^-5 T

B = 4.13 *10^-5 T

the net magnetic field is 4.13 *10^-5 T

b)
as due to i1 ,magnetic field is in z - direction

due to i2 magnetic field is in y - direction

the net magnetic field point 45 degree between y and z axis

now , angle with +ve x - axis is 90 degree

c)

angle between positive y - axis is 45 degree

d)

angle between positive z - axis is 45 degree

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