Question

You may have used a set of jumper cables connected to a running vehicle to start a car with a dead battery. Jumper cables are a matched pair of wires, red and black, joined together along their length. Suppose we have a set of jumper cables in which the two wires are separated by 1.2 cm along their 3.7 m (12 ft) length. While starting a car, the wires each carry a current of 150 A, in opposite directions. What is the force between the two wires?

Answer 1

Answer:

1.3875 Newtons

Explanation:

$i_1$ = Current in one cable = 150 A

$i_2$ = Current in other cable = 150 A

r = Radius of the cables = 1.2 cm

l = Length of the cables = 3.7 m

$\mu_0$ = Vacuum permeability = $4\pi\times 10^{-7}\ H/m$

$F=\frac{\mu_0i_1i_2\times l}{2\pi r}\\\Rightarrow F=\frac{4\pi\times 10^{-7}\times 150\times 150\times 3.7}{2\pi 0.012}\\\Rightarrow F=1.3875\ N$

The force between the two wires is 1.3875 Newtons