Question

Two parallel conducting wires of equal lengths placed distance 'd' apart carry currents 'I₁' and 'I₂' respectively in opposite directions. The resultant magnetic field at the midpoint of both the wires is ______.

(µ₀ = permeability of free space.)

Options

• `µ_0 ("I"_1 + "I"_2) //pi"d"`

• `µ_0 ("I"_1 + "I"_2) //2pi"d"`

• `µ_0 ("I"_1 - "I"_2) //2pi"d"`

• `µ_0 ("I"_1 - "I"_2) //pi"d"`

Answer 1

Two parallel conducting wires of equal lengths placed distance 'd' apart carry currents 'I₁' and 'I₂' respectively in opposite directions. The resultant magnetic field at the midpoint of both the wires is `underline( µ_0 ("I"_1 + "I"_2) //pi"d")`

Explanation:

Field due to a current-carrying long wire is given by

B =`(µ_"0""I")/(2pi"r")`

To fields at the midpoint between the two wires are in the same direction and hence get added.

The distance of the midpoint r = `"d"/2`

`therefore "B" ="B"_1 + "B"_2 = (µ_"0""I"_1)/(2pi("d"/2)) +  (µ_"0""I"_2)/(2pi("d"/2))`

` = (µ_"0"("I"_1 + "I"_2))/(pi"d")`