Question

Two long straight parallel wires carry currents 1, and I, in the same direction. Find an expression for the force per unit length between them Depict the pattern of magnetic field lines. Use the expression to define SI unit of current OR​

Answer 1

Answer:

[see image 1]

Consider two infinitely long parallel conductors carrying current I

1

and I

2

in the same direction.

Let d be the distance of separation between these two conductors.

[see image 2]

B

1

=

2πd

μ

0

I

2

F

2

=I

2

×l

2

×B

1

sinθ (sinθ=1]

⇒F

2

=I

2

×l

2

×

2πd

μ

0

×l

1

Force per unit length,

F=

2πd

μ

0

I

1

I

2

,B

2

=

2πd

μ

0

I

2

F

1

=I

1

×l

1

×B

2

sinθ

⇒F

1

=

2πd

μ

0

I

1

I

2

l

1

∵ Force per unit length, F=

2πd

μ

0

I

1

I

2

Hence, force is attractive in nature.

Ampere : Ampere is that current which is if maintained in two infinitely long parallel conductors of negligible cross-sectional area separated by 1 metre in vacuum causes a force of 2×10

−7

N on each metre of the other wire.

Then current flowing is 1A

[see image 3]

(i) Magnetic moment will be out of the plane from the surface HEFG.

(ii) Torque

(A) Torque is maximum when MII B i.e., when it gets rotated by 90

o

.

(B) Torque is minimum when M and B are at 270

o

to each other.