Two parallel wires are separated by a distance L along the x-axis, as shown belo

Question

Two parallel wires are separated by a distance L along the x-axis, as shown below. The left wire has twice the current as the right wire and is coming out of the page. Somewhere between the wires, you measure zero magnetic field.

a. Is the current in the right wire going into the page or coming out of the page? Draw a diagram below to justify your answer

b. Where is that point where B = 0? (Give its distance from the left wire.)
c. What is B (both magnitude and direction!) at point Z (in terms of µ0)?

Explanation / Answer

2I is out of page and I is into page

so

Net field at any laction will be out of page

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part B :

let Bnet be at x from 2I,

si this distance is from (L-x) from I

so at this point

B1 = B2

uo 2I/2pi X = uo I/(2pi (L-x)

2I/X = I/(L-x)

2L - 2x = X

3x = 2L

x = (2L/3) distance from 2I

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Bnet = uo (2I+I)/(2 pi * 2L/3)

Bnet = uo *9 I/ (4 pi L)

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