Question

Two long parallel wires are at a distance of 1 metre if both of them carry one ampere of current then the force of attraction per unit length between the two wires is

Answer 1

Explanation:

Force per unit length between two infinity long parallel wires is given by, \mathbb{F}=\frac{\mu_0i_1i_2}{2\pi d}F=

2πd

μ

0

i

1

i

2

where,\mu_0μ

0

is permeability of vaccum or air, i_1,i_2i

1

,i

2

are current through parallel wires respectively and d is the separation between wires.

here, \mu_0μ

0

= 4π × 10^-7 Nm/A²

i_1=i_2=2Ai

1

=i

2

=2A and d = 1m

so, \mathbb{F}F = 4π × 10^-7 × (2)²/(2π × 1)

= 2 × 10^-7 × 4

= 8 × 10^-7 N/m

but given, force per unit length is k × 10^-7 N/m

comparing both sides,

we get, k = 8