Question

80. Two infinitely long parallel wires are at a distance of 1 meter. Both of them carry 2 Ampere of

current. The force of attraction per unit length between the two wires is found to be

k*10^-7 N / m



Find k?

Answer 1

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

where,$\mu_0$ is permeability of vaccum or air, $i_1,i_2$ are current through parallel wires respectively and d is the separation between wires.

here, $\mu_0$ = 4π × 10^-7 Nm/A² $i_1=i_2=2A$ and d = 1m

so, $\mathbb{F}$ = 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

Answer 2

Explanation: Force per unit length between two infinity long parallel wires is given by,  

where, is permeability of vaccum or air,  are current through parallel wires respectively and d is the separation between wires.

here,  = 4π × 10^-7 Nm/A²

and d = 1m

so,  = 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