Problem 29.41 Part A A long wire carrying a 5.2 A current perpendicular to the r

Question

Problem 29.41 Part A A long wire carrying a 5.2 A current perpendicular to the ry-plane intersects the c-axis at z -2.0cm. A second, parallel wire carrying a 2.8 A current intersects the z-axis at z =-20cm At what point on the z-axis is the magnetic field zero if the two currents are in the same direction? Express your answer to two significant figures and include the appropriate units | Value Units Submit My Answers Give Up Part B At what point on the -axis is the magnetic field zero if the two currents are in opposite directions? Express your answer to two significant figures and include the appropriate units -ValveUnits Submit My Answers Give Up

Explanation / Answer

a) When the currents are flowing in the same direction, the 2 magnetic fields due to the 2 currents will be equal and opposite somewhere between the wires.
Since B = oI/(2r),
B1 - B2 = 0
o/(2)[I1/(x - (-2)) - I2/(2 - x)] = 0
x = 2(I1 - I2)/(I1 + I2)
x = 2(5.2A - 2.8A)/(5.2A + 2.8A)
x = 0.6cm

b) When the currents are in opposite directions, the magnetic fields due to each wire will be in opposite directions to the left of the 1st wire and to the right of the 2nd wire. The combined magnetic field to the left of the wires, however, will never be zero because the magnetic field contribution of the 1st wire, being the closest and having the higher current, will always be larger than that of the 2nd wire. So we only need to concern ourselves with some point to the right of the 2 wires:
B1 - B2 = 0
o/(2)[I1/(x + 2) - I2/(x - 2)] = 0
x = 2(I1 + I2)/(I1 - I2)
x = 2(5.2A + 2.8A)/(5.2A - 2.8A)
x = 6.67cm

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