A long straight horizontal wire carries a current = 3.90 A to the left. A positive 1.00 C charge moves to the right at a distance 1.50 m above the wire at constant speed v = 5000 m/s. What is the magnitude of the magnetic field at the location of the charge due to the current-carrying wire?
The field there will only depend upon the current in and distance from the wire. Use Ampere's law. You will find the formula at
http://www.pa.msu.edu/courses/1997spring/phy232/lectures/ampereslaw/wire.html
To find the magnitude of the magnetic field at the location of the charge due to the current-carrying wire, you can use the formula for the magnetic field created by a long straight wire:
B = (μ0 * I) / (2π * r)
Where:
- B is the magnitude of the magnetic field
- μ0 is the permeability of free space, which is a constant equal to 4π × 10^(-7) T·m/A
- I is the current in the wire
- r is the distance from the wire
From the given information, we know that the current in the wire is 3.90 A and the distance from the wire is 1.50 m.
Now, let's substitute the values into the formula:
B = (4π × 10^(-7) T·m/A * 3.90 A) / (2π * 1.50 m)
The π cancels out, and simplifying the expression gives:
B = (2 * 10^(-7) T·m/A * 3.90 A) / 1.50 m
B = (2.0 * 10^(-7) * 3.90) T
Calculating this value gives:
B = 7.8 * 10^(-7) T
Therefore, the magnitude of the magnetic field at the location of the charge due to the current-carrying wire is 7.8 * 10^(-7) T.
To find the magnitude of the magnetic field at the location of the charge due to the current-carrying wire, you can use the formula for the magnetic field produced by a current-carrying wire:
B = μ₀ * I / (2πr)
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.
In this case, the current I = 3.90 A, and the distance from the wire r = 1.50 m.
Substituting these values into the formula:
B = (4π×10⁻⁷ T·m/A) * (3.90 A) / (2π * 1.50 m)
Simplifying the equation:
B = (4π × 10⁻⁷ T·m/A) * (3.90 A) / (2π * 1.50 m)
= (4 × 3.90 × 10⁻⁷) / (2 × 1.50) T
= 2.60 × 10⁻⁷ T
Therefore, the magnitude of the magnetic field at the location of the charge is 2.60 × 10⁻⁷ T.