Question

Two long, straight wires are separated by a distance of 9.15 cm . One wire carries a current of 2.79 A , the other carries a current of 4.36 A .Is the force per meter exerted on the 4.36-A wire greater than, less than, or the same as the force per meter exerted on the 2.79-A wire

Answer 1

The force is the same

Step-by-step explanation:

The force per meter exerted between two wires carrying a current is given by the formula

`(F)/(L)=(\mu_0 I_1 I_2)/(2\pi r)`

where

`\mu_0` is the vacuum permeability

`I_1` is the current in the 1st wire

`I_2` is the current in the 2nd wire

r is the separation between the wires

In this problem

`I_1=2.79 A\\I_2=4.36 A\\r = 9.15 cm = 0.0915 m`

Substituting, we find the force per unit length on the two wires:

`(F)/(L)=((4\pi \cdot 10^(-7))(2.79)(4.36))/(2\pi (0.0915))=2.66\cdot 10^(-5)N`

However, the formula is the same for the two wires: this means that the force per meter exerted on the two wires is the same.

The same conclusion comes out from Newton's third law of motion, which states that when an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A (action-reaction). If we apply the law to this situation, we see that the force exerted by wire 1 on wire 2 is the same as the force exerted by wire 2 on wire 1 (however the direction is opposite).