Question

The wire in the drawing carries a current of 14 A. Suppose that a second long, straight wire is placed right next to this wire. The current in the second wire is 33 A. Use Ampere's law to find the magnitude of the magnetic field at a distance of r = 0.75 m from the wires when the currents are (a) in the same direction and (b) in opposite directions. Circular path (a) NumberT0.1142892063 Units (b) Number 0.0340435934 Units

Answer 1

a) Currents

I1 = 14 A

I2 = 33 A

r = 0.75 m

According to Ampere circuital law,

B.dl = uI

a)

11 12

Enclosed current, I = I1 + I2

I = 14 + 33

I = 47 A (upward)

B.dl = uI

B(2$\pi$r) = $\mu$ I

B = $\mu$ I/(2$\pi$r)

B = (2 x 10^-7 x 47)/0.75

B = 1.25 x 10^-5 T (counter-clockwise)

b)

1 12

I = I2 - I1

I = 33 - 14

Enclosed current, I = 19 A (downward)

B.dl = uI

B(2$\pi$r) = $\mu$ I

B = $\mu$ I/(2$\pi$r)

B = (2 x 10^-7 x 19)/0.75

B = 5.07 x 10^-6 T (clockwise)

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