17. Two long straight wires carry currents perpendicular to the xy plane. One wi

Question

17. Two long straight wires carry currents perpendicular to the xy plane. One wire carries a current of 30 A and passes through the point x = 7 cm on the x axis. The second wire carries a current of 20 A and passes through the point y = 6 cm on the y axis.

i) Determine the magnitude of the magnetic field at the origin due to the wire passing through the point on the x-axis.

ii) Determine the magnitude of the magnetic field at the origin due to the wire passing through the point on the y-axis.

iii) Determine the magnitude of the magnetic field at the origin due to the combined magnetic fields of the wires.

Explanation / Answer

Use Ampere's Law a couple of times to get the components of the magnetic field.
B ds = (o)I

i) (B2)(2y) = (o)(I2)
B2 = (o)(I2) / (2y)
B2 = (1.257e-6 N/A²)(20 A) / (2(0.06 m))
B2 = 6.67e-5 T (along one of the the x-axis directions)

ii) (B1)(2x) = (o)(I1)
B1 = (o)(I1) / (2x)
B1 = (1.257e-6 N/A²)(30 A) / (2(0.07 m))
B1 = 8.57e-5 T (along one of the the y-axis directions)

iii) B = sqrt[(B1)² + (B2)²]
B = sqrt[(8.57e-5 T)² + (6.67e-5 T)²]
B = 10.86*10^-5 T

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