Numerical

**Answer the following question.**

Two infinitely long straight wire A_{1} and A_{2} carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A_{3} carrying current 1.5 I be placed between A_{1} and A_{2} so that it experiences no net force due to A_{1} and A_{2}? Does the net force acting on A_{3} depend on the current flowing through it?

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#### Solution

`"F"_31 = "F"_32`

`("μ"_0("I") (1.5 "I"))/(4"π"(x)) = ("μ"_0 (1.5 "I") (2 "I"))/(4"π"(d - x))`

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

`d - x = x`

`d = 2x`

`x = d/(2)`

The net force acting on A_{3},

`|"F"_"net"| = |("μ"_0("I") ("I"_("A"3)))/(4"π"(x)) = ("μ"_0("I"_("A"3)) (2 "I"))/(4"π"(d -x))|`

Hence, it depends on the value of the current flowing through A_{3.}

Concept: Force Between Two Parallel Currents, the Ampere

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