Two parallel straight wires are 1 meter apart. Each wire carries a current of 2 Amperes in the same direction. What is the resultant magnetic field produced by both wires at a point:
2) 1/4 of the distance between them
I don't really understand what 2 is saying to be real honest.. Is it asking for 1/4 the distance as in 0.25 and 0.75 meter split?
It is not clear. It could mean
a) pick a point 1/4 the distance between them from one wire (distance to the other wire is 3/4), and compute field
b) it could mean 1/4 distance perpendicular to the line between the two wires, or else.
My guess is a)
Yes, you're correct! When it says "1/4 of the distance between them," it means the point that is one-fourth of the total distance between the two wires.
To find the resultant magnetic field produced by the wires at a point that is 1/4 of the distance between them, we can follow these steps:
1. Determine the magnetic field produced by each wire separately at the given point using the formula for the magnetic field produced by a straight wire:
B = (μ₀ * I) / (2π * r)
Where:
- B is the magnetic field
- μ₀ is the permeability of free space (equal to 4π × 10^(-7) Tesla meter per Ampere)
- I is the current
- r is the distance from the wire to the point of interest
2. Calculate the distance from each wire to the point. Since the wires are parallel, the distances from each wire to the point will be the same.
3. Add the magnetic fields produced by each wire at the point to obtain the resultant magnetic field.
Let's calculate it step by step:
Given:
Distance between the wires = 1 meter
Current in each wire = 2 Amperes
Point of interest is at 1/4 of the distance between the wires.
Step 1:
Using the formula for the magnetic field produced by a wire, let's calculate the magnetic field produced by each wire at the point.
For wire 1:
Distance from wire 1 to the point = 1/4 * 1 meter = 0.25 meters
B₁ = (μ₀ * I) / (2π * r)
= (4π × 10^(-7) * 2) / (2π * 0.25)
= (8π × 10^(-7)) / (0.5π)
= (8 × 10^(-7)) / (0.5)
= 16 × 10^(-7) Tesla
= 16 μT (microtesla)
For wire 2:
Distance from wire 2 to the point = 1/4 * 1 meter = 0.25 meters
B₂ = (μ₀ * I) / (2π * r)
= (4π × 10^(-7) * 2) / (2π * 0.25)
= (8π × 10^(-7)) / (0.5π)
= (8 × 10^(-7)) / (0.5)
= 16 × 10^(-7) Tesla
= 16 μT (microtesla)
Step 2:
Since the wires are 1 meter apart, the distances from each wire to the point are equal. In this case, both distances are 0.25 meters.
Step 3:
To get the resultant magnetic field at the point, we need to add the magnetic fields produced by each wire. Since they are in the same direction, we simply add them.
Resultant magnetic field = B₁ + B₂
= 16 μT + 16 μT
= 32 μT
Therefore, the resultant magnetic field produced by both wires at a point that is 1/4 of the distance between them is 32 μT (microtesla).