Question

Answer the following question.
Two infinitely long straight wire A₁ and A₂ carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A₃ carrying current 1.5 I be placed between A₁ and A₂ so that it experiences no net force due to A₁ and A₂? Does the net force acting on A₃ depend on the current flowing through it?

Answer 1

The force per unit length between two infinitely long, parallel current-carrying wires is given by:

`F = μ_0/(2pi) (I_1I_2)/d`

where:

• I₁​ and I₂​ are the currents in the wires,
• d is the separation between them,
• μ₀ is the permeability of free space.

Assigning Given Values

• A₁​ carries current I.
• A₂​ carries current 2I.
• The distance between A₁​ and A_2​ is d.
• A_3​ carries current 1.5I and is to be placed somewhere between A₁​ and A_2​.

For A₃​ to experience zero net force, the magnitudes of these forces must be equal:

F₁ = F₂

`μ_0/(2pi) (Ixx1.5I)/x = μ_0/(2pi) (2Ixx1.5I)/((d-x)`

`(1.5I^2)/x = (3I^2)/(d-x)`

`1/x = 2/(d-x)`

d − x = 2x

d = 3x

`x = d/3`