A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects th

Question

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis atx=2.0cm. A second, parallel wire carrying a 3.5 A current intersects the x-axis atx=+2.0cm. Part A At what point on the x-axis is the magnetic field zero if the two currents are in the same direction? Express your answer using two significant figures. Part B At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions? Express your answer using two significant figures.

Explanation / Answer

(A) Magnetic field due to long wire,

B = 0*I/(2*pi*r)

Assume that at one point, Btotal = 0, which is x distace from one wire and 4-x from second wire.

Hence,

B1 = B2

0*I1/(2*pi*x) =0*I2/(2*pi*(4-x))
I1/x = I2/(4-x)
6/x = 3.5/(4 - x)

24-6x =3.5 x

x =24/9.5
---> r = 2.526 cm

the point is at 8/3 cm to the right of the left wire
Co-ordinate on axis,

= 2.526 - 2 = 0.526 cm (on the +x axis)

(B)
For, opposite current flow, the point where magnetic field is zero, cant be in center,
6/(x+ 4) = 3.5/x

6x =3.5 x + 14
x = 5.6 cm
The point is x+2 =7.6 cm on x axis.

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