Two infinitely long

PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism

Problem

Two infinitely long, parallel conductors are placed along the

z

-axis at the points

A(-\tfrac{d}{2},0)

and

B(\tfrac{d}{2},0)

in the

xy

-plane. Conductor

A

carries a steady current

I

and conductor

B

carries a steady current

2I

, both directed out of the page. (i) Obtain an expression for the magnitude of the resultant magnetic field at a general point

P(x,y)

in the plane. (ii) Hence show that the locus of points for which the magnitude of the resultant field equals

\displaystyle \frac{\mu_0 I}{4\pi d}

is a circle and find its centre and radius. (iii) Sketch qualitatively the position of this circle with respect to the two conductors.