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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?
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Solution
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 A2 is d.
- A3 carries current 1.5I and is to be placed somewhere between A1 and A2.
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`
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