Ten meters away from a long straight wire, the field is 10-4 (10 to the negative four) Tesla. What current flows through the wire?
I know the answer is 5.0kA but I am not sure what formula to use.
To determine the current flowing through the wire, you can use the equation for the magnetic field produced by a long straight wire, which is given by the formula:
B = (μ₀ * I) / (2π * r),
where B is the magnetic field, μ₀ is the magnetic constant (equal to 4π × 10^-7 T·m/A), I is the current flowing through the wire, and r is the distance from the wire.
Given that the magnetic field (B) is 10^(-4) T and the distance (r) is 10 m, we can rearrange the equation and solve for I as follows:
10^(-4) T = (4π × 10^(-7) T·m/A * I) / (2π * 10 m).
Simplifying the equation gives:
10^(-4) T = (2 * 10^(-7) T·m/A * I) / 10 m.
Cross-multiplying further yields:
10^(-4) T * 10 m = 2 * 10^(-7) T·m/A * I.
Finally, solving for I gives:
I = (10^(-4) T * 10 m) / (2 * 10^(-7) T·m/A).
Calculating the right side of the equation gives:
I = (10^(-3) T·m²/A) / (2 * 10^(-7) T·m/A).
Simplifying the expression further, we get:
I = 5 * 10^3 A.
Therefore, the current flowing through the wire is 5.0 kA (kilamperes).
To determine the current flowing through the wire, you can use Ampere's Law. This law states that the magnetic field at a point near a straight current-carrying wire is directly proportional to the current through the wire and inversely proportional to the distance from the wire.
The equation for calculating the magnetic field (B) at a distance (r) from a long straight wire carrying current (I) is given by:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field in Tesla (T)
μ₀ (mu naught) is the permeability of free space, which is a constant value of 4π x 10⁻⁷ Tm/A
I is the current in Amperes (A)
r is the distance from the wire in meters (m)
In your case, the magnetic field (B) is given as 10⁻⁴ T, and the distance (r) is 10 meters. We can rearrange the formula to solve for the current (I):
I = (B * 2π * r) / μ₀
Substituting the given values:
I = (10⁻⁴ T * 2π * 10 m) / (4π x 10⁻⁷ Tm/A)
Simplifying:
I = (2π * 10⁴) / (4π x 10⁻⁷) A
I = 5.0 x 10³ A
Therefore, the current flowing through the wire is 5.0 kilo-Amperes (kA).