The drawing shows two perpendicular, long, straight wires, both of which lie in

Question

The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. The current in each of the wires is I = 6.2 A. Find the magnitudes of the net magnetic fields at points A and B. (Assume that r1 = 0.22 m and r2 = 0.38 m.)

The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. The current in each of the wires is

I = 6.2 A.

Find the magnitudes of the net magnetic fields at points A and B. (Assume that

r1 = 0.22 m

and

r2 = 0.38 m.)

Explanation / Answer

For a straight current-carrying wire,
B dL = (µo)(I)
B(2r) = (µo)(I)
B = (µo)(I) / (2r)

Using right-hand rule, the magnetic field components due to the separate wires will get subtracted from each other at both points A and B. Since the distances from the wires are the same, the magnitude of the magnetic field will be the same at A and B, though in opposite directions.

Br1 = (4 x 10-7 N/A²)(6.2 A) / (2(0.22 m))
Br1 = 5.63 x 10-6 T

Br2 = (4 x 10-7 N/A²)(6.2 A) / (2(0.38 m))
Br2 = 3.26 x 10-6

(5.63 x 10-6  - 3.26 x 10-6) T

= 2.37 x 10-6 T

or,

= 2.37 µT

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