Two straight paralle wires carry currents in opposite directions as shown in the

Question

Two straight paralle wires carry currents in opposite directions as shown in the figure. One of the wires carries a current of I2 = 11.4 A. Point A is the midpoint between the wires. The total distance between the wires is d = 11.1 cm. Point C is 5.34 cm to the right of the wire carrying current I2. Current I1 is adjusted so that the magnetic field at C is zero. Calculate the value of the current I1. Tries 0/20 Calculate the magnitude of the magnetic field at point A. Tries 0/20What is the force between two 2.27 m long segments of the wires?

Explanation / Answer

given,

I2 = 11.4 A

d = 11.1 cm

point C is 5.34 cm right to wire carrying current I2

magnetic field due to current carrying wire = k * I / r

magnetic field due to wire 2 = 2 * 10^-7 * 11.4 / (0.0534)

magnetic field due to wire 1 = 0.0000426966 T

in order to have net magnetic field 0 at point C the magnetic field due to wire had to be equal to the magnetic field due to wire 2

magnetic field due to wire 1 = 2 * 10^-7 * I1 / (0.111 + 0.0534)

2 * 10^-7 * I2 / (0.111 + 0.0534) = 0.0000426966

I1 = 35.09 A

magnitude of magnetic field at A = k (i1 + I2) / (d/2)

magnitude of magnetic field at A = 2 * 10^-7 * (35.09 + 11.4) / (0.111/2)

magnitude of magnetic field at A = 0.0001675 T

force = k * i1 * i2 * length / d

force = 2 * 10^-7 * (35.09 * 11.4) / (0.111) * 2.27

force = 0.00164 N

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