Question

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

Answer 1

Magnetic field due to a current carrying at a point is given by:

B = u0*I/(2*pi*r)

Since both wire have currents in opposite direction, So magnetic field cannot be zero between both wires because net magnetic will be sum of magnetic field due to both wires.

Since magnetic field is directly proportional to current in wire, So in this case wire 2 have smaller current, So net magnetic field will be zero towards right of wire 2

Now Suppose

B_net = 0

B1 - B2 = 0

B1 = B2

u0*I1/(2*pi*r1) = u0*I2/(2*pi*r2)

I1/r1 = I2/r2

r2 = d (d distance from wire 2)

then, r1 = 4 + d

I1 = 5.5 A and I2 = 2.0 A, So

5.5/(4 + d) = 2.0/d

5.5*d = 8 + 2*d

3.5*d = 8

d = 8/3.5 = 2.29 cm

So magnetic field will be zero at x = 2.0 + 2.29 = 4.29 cm = 0.429 m

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