Question

The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.335 N/m.

Required:
a. What is the current in the wires, given they are separated by 2.90 cm?
b. Is the force attractive or repulsive?

1. The force is repulsive because the currents are in opposite directions.
2. The force is repulsive because the currents are in the same direction.
3. The force is attractive because the currents are in the same direction.
4. The force is attractive because the currents are in opposite directions.

Answer 1

a) I = 1.29 10⁻⁴ A , b) the current has the opposite direction in each cable, therefore the correct answer must be 1

Step-by-step explanation:

a) Let's analyze this exercise, when a conductor carries a current the elctoenes generate a magnetic field around the cable and this field can interact with the electrons that carry a current in a nearby cable, the expression for force is

F₁ = I₁ L B₂

where F₁ is the force on a cable through the field created by elotorcable.

The field sent by the other cable is

B₂ = μ₀ I² / 2πa

we substitute

F₁ = μ₀ I₁ I₂ / 2πa L

suppose the current in the two cables is the same

I₁ = I₂ = I

F₁ / L = μ₀ I₂ / 2πa

i = √ [(F₁ / L) 2πa / μ₀]

let's calculate

I = √ [0.335 2 π / 4π 10⁻⁷]

I = √ [0.335 / 2 10⁷]

I = 1.29 10⁻⁴ A

b) if the two cables have the current in the same direction the force is attractive and if it has the current in the opposite direction it is negative

the two possible answers are 1 and 2

In general, to start a car, one of the cables has a current from the battery at start-up and the other cable comes from the start to the battery, therefore the current has the opposite direction in each cable, therefore the correct answer must be 1