Two long straight parallel wires 99 cm aarry currents of equ

Two long, straight, parallel wires 9.9 cm aarry currents of equal magnitude I. They repel each other with a force per unit length of 4.5 nN/m. Find the current I. A

Solution

magnetic field due to one wire at the location of another wire,

B = u0 I / (2 pi d)

direction of field will be perpendicular to the current and page containing both wires.

and force on current wire,

F = IL X B

IL and B are perpendicular hence

F = I L B = ( I L ) (u0 I / 2 pi d )

F/L = u0 I^2/ 2pi d

4.5 x 10^-9 = (4pi x 10^-7 x I^2) / (2 pi x 0.099)

I = 0.0188 A