Two 10 meter long wires are parallel to each other and 5 cm apart.They carry currents of 6.0 A in opposite directions. What is the magnitude and direction of the magnetic field at a point P,halfway between the wires?
Calculate the force exerted by the left wire on the right wire. Indicate the direction of the force.
Parallel wires with currents in the same direction are attracted to each other. If the currents are in opposite directions, they repel.
If the currents are in opposite directions, the magnetic field along a line midway between them is twice the field due to a single wire.
The formulas you need can be found here:
http://theory.uwinnipeg.ca/physics/mag/node10.html
To find the magnitude and direction of the magnetic field at point P, halfway between the wires, we can use the Biot-Savart Law. The Biot-Savart Law states that the magnetic field created by a current-carrying wire at a point is directly proportional to the current and inversely proportional to the distance from the wire.
Here's how to apply the Biot-Savart Law to this scenario:
1. Determine the magnetic field created by each wire separately at point P. We can use the formula:
B = (μ₀ * I) / (2π * r)
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^(-7) T·m/A), I is the current, and r is the distance from the wire.
For the wire on the left, the distance from point P is 5 cm or 0.05 m, and the current is 6.0 A. Plugging these values into the formula, we get:
B₁ = (4π × 10^(-7) * 6.0) / (2π * 0.05) = 0.024 T
Likewise, for the wire on the right, the magnetic field is also 0.024 T.
2. Since the wires are carrying currents in opposite directions, the magnetic fields they create will have opposite directions as well. Therefore, the magnetic field from the left wire is directed into the page (towards you), and the magnetic field from the right wire is directed out of the page (away from you).
3. To find the total magnetic field at point P, we add the two magnetic fields:
B(total) = B₁ + B₂ = 0.024 T + (-0.024 T) = 0 T
The total magnetic field at point P is 0 T, indicating that the magnetic fields created by the wires cancel each other out.
Now let's move on to calculating the force exerted by the left wire on the right wire:
1. The force between two parallel current-carrying wires can be found using the formula:
F = (μ₀ * I₁ * I₂ * L) / (2π * d)
where F is the force, 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. For the left wire, the current is 6.0 A, the length is 10 m, and the distance from the right wire is 5 cm or 0.05 m. Plugging these values into the formula, we get:
F₁ = (4π × 10^(-7) * 6.0 * 6.0 * 10) / (2π * 0.05) = 0.144 N
The force exerted by the left wire on the right wire is 0.144 N.
3. The direction of the force can be determined using the right-hand rule. If you point your right thumb in the direction of the current in the left wire (from left to right), and your fingers curl in the direction of the current in the right wire (from right to left), your palm will face upwards. Therefore, the force between the wires is directed upward.
In summary, the magnitude of the magnetic field at point P is 0 T, and the force exerted by the left wire on the right wire is 0.144 N, directed upward.