Question

A long wire carrying a 5.5 A current perpendicular to the xy-plane intersects the x-axis at x=- 2.0 cm . A second, parallel wire carrying a 2.5 A current intersectsthe x-axis at x= 2.0 cm.
At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

Answer 1

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/(2?r), B1 - B2 = 0 ?o/(2?)[I1/(x - (-2)) - I2/(2 - x)] = 0 x = 2(I1 - I2)/(I1 + I2) x = 2(5A - 3A)/(5A + 3A) x = 0.5cm b) When the currentsare 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 2ndwire. 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 theclosest 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 rightof the 2 wires: B1 - B2 = 0 ?o/(2?)[I1/(x + 2) - I2/(x - 2)] = 0 x = 2(I1 + I2)/(I1 - I2) x = 2(5A + 3A)/(5A - 3A) x = 8.0cm

Answer 2

the magnetic field is zero at .33cm from origin or (3.33,0)

Answer 3

two magnetic field cancel each other,and hence zero magnetic field at

5.5/r = 2.5/(4-r)
solving

220 - 55r = 25r
80r = 220
r = 2.75 cm
so at x = -2 + 2.75 = 0.75 cm , magnetic field is zero

Answer 4

Current will be zero at:

5.5/r = 2.5/(4-r)

220 - 55r = 25r
80r = 220
r = 2.75 cm
Therefore at x = -2 + 2.75 = 0.75 cm , magnetic field is zero

Answer 5

the magnetic field is zero at 3.33cm from origin or (3.33,0) when currents are in opposite direction