Magnetic forces on two current carrying wires

In summary, the force per unit length on each of the two long, straight, parallel wires that are 24 cm apart when one carries a current of 2.0 A and the other carries a current of 4.0 A in the same direction is 6.7 * 10^-6 N/m. The force is attractive between the two wires. This is obtained by using the equation F/L = IB for each wire and plugging in the respective values for current and magnetic field.
  • #1
endeavor
176
0
"Find the force per unit length on each of two long, straight, parallel wires that are 24 cm apart when one carries a current of 2.0 A and the other a current of 4.0 A in the same direction."

Tell me if I'm doing this right:
I use d = 0.24m, and the equations B = (mag. perm. * I)/(2*pi*d), and F = ILB.

The force per unit length on each wire is then: F/L = IB.

Plugging in I and B for each of the wires, I get:
F/L (for the 2.0A wire) = 3.3 * 10^-6 N/m (toward the other wire)
F/L (for the 4.0A wire) = 1.3 * 10^-5 N/m (toward the other wire)

I think it's wrong because the answer is supposedly: "6.7 * 10^-6 N/m; attractive". But I would think that the forces are different on each wire, because the wires are carrying different currents...
 
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  • #2
Your formulae are correct, however I can't see how you obtained your two different answers.
Remember, the expression you wrote explicitly is
[tex]\frac{\mu_0I_1I_2}{2\pi d}[/tex]

Can you possibly have two different answers ? :)
 
  • #3
oh ooops.
I did (F/L)1 = I1B1, not I1B2!
 
  • #4
Thought so :biggrin:
 

1. How do you calculate the magnetic force between two current-carrying wires?

The magnetic force between two parallel current-carrying wires can be calculated using the formula F = (μ0 * I1 * I2 * L) / (2πd) where μ0 is the permeability of free space, I1 and I2 are the currents in the wires, L is the length of the wires, and d is the distance between the wires.

2. What factors affect the strength of the magnetic force between two current-carrying wires?

The strength of the magnetic force between two current-carrying wires is affected by the currents in the wires, the distance between the wires, and the permeability of the medium between the wires.

3. How does the direction of the currents in the wires affect the magnetic force between them?

The direction of the currents in the wires affects the direction of the magnetic force between them. If the currents are flowing in the same direction, the force will be attractive, but if the currents are flowing in opposite directions, the force will be repulsive.

4. Can the magnetic force between two current-carrying wires be measured?

Yes, the magnetic force between two current-carrying wires can be measured using a device called a force balance or by using a digital multimeter to measure the current in the wires.

5. What is the relationship between the magnetic force and the distance between the wires?

The magnetic force between two current-carrying wires is inversely proportional to the distance between the wires. This means that as the distance between the wires increases, the force decreases, and vice versa.

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