Question

8.7. A conducting strip of infinite length lies in the xy plane with its length oriented along the x axis, and where – b/2<y<b/2 defines its width along y. Current I flows down the strip in the positive x direction and is uniformly distributed over the width. Above the strip and parallel to it at z=d is an infinitely long current filament that carries current I in the positive x direction. Find the force of attraction between the two currents per unit length in X. Assume d<b.

Answer 1

The current I₁ is uniformly distrubuted over the strip in +X direction and the filament is at a height d from the strip, a current I₂ is flowing in the +X direction in the filament, the strip is of width b and length of infinity.

We know the magnetic field of a sheet of uniformly distributed current is, B₀, the value of B₀ is given below,

AL 27 11 k=k -мок і 37 7б Bo X + Пок j zo 9

K is the surface current density.

So the relation between uniform K and I₁ in the strip is like this,

Iq=kb b

Subsituting in B₀ we get the magnetic field due to the strip in the +Z direction,

- Con = 8

So, the force on the filament per unit length is given as,

1. І Bo I2 أ Но І. 2b - І, мо 11 25

Indeed its direction is at the -Z direction therefore it is an attractive force.