   Chapter 19, Problem 56P

Chapter
Section
Textbook Problem

Two parallel wires separated by 4.0 cm repel each other with a force per unit length of 2.0 × 10−4 N/m. The current in one wire is 5.0 A. (a) Find the current in the other wire. (b) Are the currents in the same direction or in opposite directions? (c) What would happen if the direction of one current were reversed and doubled?

a)

To determine
The current in the second wire.

Explanation

Given info: The separation between the two wires is 4.0cm . The force per unit length between the wires is 2.0×104Nm-1 . The current in one wire is 5.0A .

Explanation:

Force per unit length between two parallel current carrying wires is,

Fl=μ0I1I22πd

• Fl is the weight per unit length
• I1 is the current in the one wire
• I2 is the current in the second wire
• d is the distance between the wires
• μ0 is the permeability of free space

On rearrangement for current,

I2=F2πdlμ0I1

Substitute 4π×107TmA-1 for μ0 , 4.0cm for d , 5.0A for I1 , 2.0×104Nm-1 for Fl to determine the current in the second wire,

I2=2π(2

b)

To determine
Whether the currents are in the same or opposite direction.

c)

To determine
What happens when the direction of the one current were reversed and doubled.

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