Question

Derive an expression for the force of interaction between two parallel wires carrying current. Use the expression to define S.I. unit of current.​

Answer 1

Let the distance between the two conductors carrying current I

1

and I

2

be d.

Magnetic field produced by conductor 1 at a distance d, B

1

=

4π

μ

o

d

2I

1

Force acting the conductor 2 placed in this magnetic field F=B

1

I

2

L

Thus we get F=

4π

μ

o

d

2I

1

I

2

L

Force er unit length of conductor 1 f=

4π

μ

o

d

2I

1

I

2

Now put d=1m, I

1

=I

2

=1A and L=1m

We get F=

2π

μ

2

=2×10

−7

N

Thus we define ampere as the current flowing in each conductor separated by a unit distance so that one conductor applies a force of 2×10

−7

N on a unit length of another parallel conductor.

Answer 2

Parallel currents attract, antiparallel currents repel.