Two long parallel wires are separated by a distance of 2 . 50   cm . The force per unit length that each wire exerts on the other is 4 × 10 - 5   N   m - 1 , and the wires repel each other. The current in one wire is 0 . 5   A . What is the current in the second wire?…

Question

Two long parallel wires are separated by a distance of 2 . 50 &#160; cm . The force per unit length that each wire exerts on the other is 4 &#215; 10 - 5 &#160; N &#160; m - 1 , and the wires repel each other. The current in one wire is 0 . 5 &#160; A . What is the current in the second wire? (Take &#956; 0 = 4 &#960; &#215; 10 - 7 S.I. Unit)

Aicharya · Accepted Answer

The formula of force between two current-carrying wire placed parallel to each other in terms of current in each wire and separation between two wires is,
$F = \frac{μ_{0}}{2 π r} \times i_{1} i_{2} \times l$ , the value is given,
$\frac{F}{l} = 4 \times 10^{- 5} N m^{- 1}$ ,

$\Rightarrow \frac{F}{l} = \frac{μ_{0}}{2 π r} \times i_{1} i_{2} \Rightarrow i_{2} = \frac{F}{l \times \frac{μ_{0}}{2 π r} \times i_{1}} \Rightarrow i_{2} = \frac{4 \times 10^{- 5} \times 2.50 \times 10^{- 2}}{2 \times 10^{- 7} \times 0.5} = \frac{2 \times 2.50}{0.5} = 10 A$

Two long parallel wires are separated by a distance of 2 . 50   cm . The force per unit length that…

Solution

Two long parallel wires are separated by a distance of 2 . 50 &#160; cm . The force per unit length that…

Solution

Two long parallel wires are separated by a distance of 2 . 50 cm . The force per unit length that…