7/28/2019 Force Between Two Parallel Conductors

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FORCE BETWEEN TWO PARALLEL CONDUCTORS:

Consider two long thin straight parallel conductors I and II placed in vacuum at a distance r

apart. Let i1and i2be the currents flowing through the conductors in the same direction. Due to

the current i1, The magnetic induction at a distance r from

the first conductor is

B1perpendicular into the plane of the paper

Now the force acting on secondconductor of a length l due to B1is

=

Similarly, the field of induction produced by the second conductor is

The force on a length l of conductor II due to B2 is

=

Force per unit length is

The two forces will be equal and opposite. Hence, the conductors attract each other. If the

direction of either current is reversed, the forces will be in opposite directions. Thus, the parallelconductors carrying current in opposite directions repel each other.

1

1

2

oi

B

r

2 2 1F i lB 1

2

2

oi

i lr

1 2

2

oi i

lr

2 1 2

2

oF i i

l r

2

2

2

oi

Br

1 1 2F i lB 2

1

2

oi

i lr

1 2

2

oi i

lr

1 1 2

2

oF i i

l r