Two long, parallel wires separated by 50 cm each carry currents of 3.0 A in a horizontal direction.
Find the magnetic field midway between the wires if the currents are in the same direction.
B= T
Find if they are in opposite directions.
B= T
Have you heard of Ampere's law? That is what you need to use.
http://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law
The answer should be obvious for the same-direction case. For the opposite-direction case, double the field due to a single wire.
To find the magnetic field midway between the wires, we can use the formula for the magnetic field produced by a current-carrying wire:
B = (μ₀ * I) / (2πd)
where:
B is the magnetic field strength,
μ₀ is the permeability of free space (4π × 10^-7 T·m/A),
I is the current in the wire, and
d is the distance from the wire.
In this case, we have two parallel wires carrying currents in the same direction. The distance between the wires is given as 50 cm.
Since the wires are parallel and the currents are in the same direction, the magnetic fields generated by each wire will be in the same direction and will add up.
So, the total magnetic field at the midpoint between the wires is:
B_total = B_wire1 + B_wire2
B_total = [(μ₀ * I) / (2πd)] + [(μ₀ * I) / (2πd)]
B_total = (2 * μ₀ * I) / (2πd)
B_total = (μ₀ * I) / (πd)
Now, we can calculate the magnetic field:
B = (μ₀ * I) / (πd)
B = (4π × 10^-7 T·m/A) * (3.0 A) / [(π * 0.5 m)]
B = (4 * 3.0 × 10^-7) / (0.5)
B = 2.4 × 10^-6 T
So, the magnetic field midway between the wires when the currents are in the same direction is approximately 2.4 × 10^-6 T.