Question

Constants Part A Three parallel wires each carry current 4.3 A in the directions shown in the figure. (Figure 1) The separation between adjacent wires is 3.34 cm Calculate the magnitude of the net magnetic force per unit length on the top wire alue Units Submit Request Answer Figure 1 of 1> Part B What is its direction? Upward Downward O The force is zero Submit

Answer 1

Part A
We have to find the net magnetic field on the top wire from the second and third wire.
The magnetic field due to the second wire
B₂ = $\mu$ ₀ I / 2 $\pi$ d
Where d is the distance between the wires. The magnetic field is directed into the plane at the top wire.
The magnetic field due to the third wire
B₃ = $\mu$ ₀ I / 2 $\pi$ (2d)
This is directed out of the plane at the top wire.
The net magnetic field at the top wire
B = B₂ - B₃ = ( $\mu$ ₀ I / 2 $\pi$ d - $\mu$ ₀ I / 4 $\pi$ d )
B = 3 $\mu$ ₀ I / 4 $\pi$ d
Directed into the plane of the paper.
The force experienced by the top wire is
F = B I L
Force per unit length of the top wire.
F / L = B I = 3 $\mu$ ₀ I² / 4 $\pi$ d
Part B
The magnetic field is directed into the plane, the current in the top wire is towards the right. According to the right hand rule, the direction of the force is upward
Part C
The magnetic field due to the top wire and the mangetic field due to the bottom wire are equal in magnitude and directed opposite to each other. So the net magnetic field at the middle wire is zero.
So the force experienced by the middle wire is also zero.
F = 0
Part D
The force is zero.
Part E
The magnetic field at the bottom wire due to the top wire,
B₁ =   $\mu$ ₀ I / 2 $\pi$ (2d)
This is directed into the plane at the bottom wire.
The magnetic field at the bottom wire due to the middle wire.
B₂ =    $\mu$ ₀ I / 2 $\pi$ d
This is directed out of the plane at the bottom wire.
So the net magnetic field
B = B₂ - B₁ = 3 $\mu$ ₀ I / 4 $\pi$ d
Directed out the plane of the paper.
The force experienced by the bottom wire is
F = B I L
Force per unit length of the bottom wire.
F / L = B I = 3 $\mu$ ₀ I² / 4 $\pi$ d
Part F
Since the magnetic field is directed out of the plane, the current in the bottom wire is directed towards the right, the magnetic force is directed downwards.