Question

Two long parallel wires, separated by a distance R have equal current I flowing in each of them. The magnetic field of one exerts a force F on the other. The distance R is increased to 4R and the current in each wire is reduced from I to I/4. What is the force between them now?

विकल्प

• 4 F

• 64 F 

• F / 4

• F / 64

Answer 1

F / 64

Explanation:

The force per unit length is,

`"F'"/"L" = mu_0/(4 pi) xx (2  "I"^2)/"R"`

If R is increased to 4R and I is reduced to I/4, the force per unit length becomes,

`"F'"/"L" = mu_0/(4 pi) xx (2("I"//4)^2)/(4"R")`

`= mu_0/(4 pi) xx (2 "I"^2)/"R" xx 1/64 = "F"/(64 "L")`

`therefore "F'" = "F"/64`