The force per meter between the two wires of a jumper cable being used to start

Question

The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.263 N/m. (a) What is the current (in A) in the wires, given they are separated by 2.50 cm? (b) Is the force attractive or repulsive? The force is attractive because the currents are in the same direction. The force is attractive because the currents are in opposite directions. The force is repulsive because the currents are in the same direction. The force is repulsive because the currents are in opposite directions.

Explanation / Answer

Given that,

F/L = 0.263 N/m

a)The magnetic force per unit length of attraction/repulsion between two wires is given by:

F/L = u0 I1 I2/2 pi R

where, I1 and I2 are the magnitudes of currents in the wires, R is the distance between them

I1 = I2 = I

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

I = sqrt [(F/L) 2 pi R/u0]

I = sqrt [0.263 x 2pi x 0.025/4 pi x 10^-7] = 181.31 A

Hence, I = 181.31 A

b)The force is repulsive because the currents are in apposite direction.

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