Question

If the distance between two current carrying wire is doubled then force between them is

Answer 1

Answer:

The force acting on one wire due to currents through two wires is inversely proportional to the distance between them. Thus the force becomes 1/2 times if the distance between the wires is doubled.

Answer 2

Answer:

If the given distance between two current-carrying wires is doubled then the respective force between them is halved.

Explanation:

Here we have been given that the distance between the two current-carrying wires has been doubled.

The force between the two current-carrying wires is given by the following formula:

F = μ₀$I_{1} I_{2} l$ / 2πd

here we have,

$I_{1}$ and $I_{2}$ are the currents in the two respective wires carrying current and d is the distance between both of them, l is the length of the wire and μ₀ is the permeability in free space.

From here we can infer that,

F ∝ $\frac{1}{d}$

As rest all quantities are same.

Now we have,

$F_{1}$ = the force at distance d

$F_{2}$ = the force at distance 2d

∴ $\frac{F_{1}}{F_{2}} = \frac{2d}{d}$

⇒ $\frac{F_{1}}{F_{2}} = \frac{2}{1}$

⇒ $F_{2} = \frac{F_{2} }{2}$

Therefore if the distance between the two current-carrying wires is increased the force between them is halved.