help with these please A long wire carrying I_A = 5.5 A of current perpendicular
ID: 1601731 • Letter: H
Question
help with these please
A long wire carrying I_A = 5.5 A of current perpendicular to the xy-plane intersects the x-axis at x = - 2.0 cm. A second, parallel wire carrying I_B = 2.0 A of current intersects the x-axis at x = +2.0 cm. (As illustrated in the figure, the two currents are either into or out of the page.) (Figure 1) At what point on the x-axis is the net magnetic field zero if the two currents are in the same direction? Express your answer using three significant figures. At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions? (Figure 1) Express your answer using three significant figures.Explanation / Answer
the magnetic field of a wire in distance r is
B = 0*I/(2pir)
(A)
let the distance of the point where Bnet = 0 from the left wire = r, the distance to the right wire is then (4 - r ) cm
B1 = B2 :
I1/(r) = I2/(4 - r)
5.5/r = 2/(4 - r)
---> r = 2.93cm
the point is at 6.286 cm to the right of the left wire
---> at x = 2.93 - 2 = .93 cm (on the +x axis)
The fields at this point between the wires are in opposite directions when the directions of the currents are equal, as we are at different sides of the wires.
(B)
When the currents are in equal directions, the point where the fields are in opposite directions is on the same side of the wires.
So let r = the distance of the point from the right wire into the +x direction. The distance to the left wire is then (4 + r) cm:
5.5/(r+ 4) = 2/r
---> r = 2.286 cm
---> the point is 2.286 cm to the right of the right wire = at x = 4.286 cm (on the +x axis)
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