Determining the current in wires based on the magnetic field.?

Question

A long straight wire carries a current of I1= 12A into the plane of paper. A second wire is 10m from the first and parallel to it.

a) What are the magnitude and direction of the current I2 in the second wire if the magnetic field is zero at a point between them in the plane containing both wires, 2 m from the first.

b) Part (a) can be answered by first finding the field of the first current. What is the advantage of not doing that, and first developing a relation between I1 and I2.

Thanks!

Answer 1

a)  B = B1 + B2

B = mu I / (2 pi r)

at a point r = 2 from the first the field is 0 thus

0 = mu / (2 pi) ( 12/2 - I/10)

Solve for I: 12/2 = I/10 => I = 60 A out of the plane

b) The advantages of solving the equation by using an algebraic expression as shown in the solution for part a allows for the cancellation of the fundamental constants mu and pi - this means you can do the question without using a calculator.