Question

Two thin long parallel wires separated by a distance b are carrying currents of 1 amp. each.
The magnitude of the force per unit length exerted by one wire over the other is
दो पतले एवं लम्बे समांतर तारों में, जिनके बीच की दूरी b है, I ऐम्पियर की धारा प्रत्येक
में प्रवाहित होती है। इसमें एक तार द्वारा दूसरे तार पर प्रति इकाई लंबाई पर लगने वाला
बल होगा:
(b) Hi
62
27b
Hai
(d)
2zb
2rba
​

Answer 1

• The magnitude of the force per unit length exerted by one wire over the other is u₀i²/2πb

Magnetic field due to infinite wire can be calculated by -

B= u₀i/2πr where i is the current flow in the wire and r is the distance between the two wires.

So, magnetic field due to wire A at distance b⇒ B= u₀i/2πb

Force on the wire due to field A is given by

F=iB.dl

F= i $\frac{uo i}{2\pi l}$ . dl

F/dl= u₀i²/2πb

Refer to the diagram from more details.