A long, straight wire carries a current of 48 A. The magnetic field produced by this current at a certain point is 6.5 10-5 T. How far is the point from the wire?
To determine the distance of the point from the wire, you can use the formula for the magnetic field produced by a long, straight wire at a point:
B = (μ0 * I) / (2π * r)
where:
B is the magnetic field in Tesla (T),
μ0 is the permeability of free space (4π * 10^-7 T m/A),
I is the current in Amps (A), and
r is the distance from the wire in meters (m).
Rearranging the formula, we can solve for r:
r = (μ0 * I) / (2π * B)
Substituting the given values:
μ0 = 4π * 10^-7 T m/A
I = 48 A
B = 6.5 * 10^-5 T
r = (4π * 10^-7 T m/A * 48 A) / (2π * 6.5 * 10^-5 T)
r = (1.92 * 10^-5 T m²/A) / (1.3 * 10^-5 T)
r = (1.92 / 1.3) * 10^-5 m²/A
Calculating this:
r ≈ 1.48 * 10^-5 m²/A
Therefore, the point is approximately 1.48 * 10^-5 meters (or 14.8 micrometers) away from the wire.
To find the distance between the point and the wire, we can use the Biot-Savart Law. The Biot-Savart Law states that the magnetic field (B) produced by a current-carrying wire is directly proportional to the current (I) and inversely proportional to the distance (r) from the wire.
The formula for the magnetic field produced by a straight wire is given by:
B = (μ₀/2π) * (I/r)
Where:
B = Magnetic field (in Tesla)
μ₀ = Magnetic constant (4π * 10⁻⁷ T m/A)
I = Current (in Amperes)
r = Distance from the wire (in meters)
To find the distance (r), we rearrange the formula as follows:
r = (μ₀/2π) * (I/B)
Substituting the given values:
μ₀ = 4π * 10⁻⁷ T m/A
I = 48 A
B = 6.5 * 10⁻⁵ T
r = (4π * 10⁻⁷ T m/A) / (2π) * (48 A / 6.5 * 10⁻⁵ T)
Simplifying the equation:
r = (4π * 10⁻⁷ T m/A) / (2π * 48 A / 6.5 * 10⁻⁵ T)
r = (4π * 10⁻⁷ T m/A) / (12.96*10⁻⁴ T m/A)
Now, we can cancel out the units:
r = (4π) / (12.96*10⁻⁴)
= 12.27 * 10⁻⁴
Therefore, the distance of the point from the wire is approximately 12.27 * 10⁻⁴ meters.
Look up Ampere's law for the magnetic field around a straight wire.
You can find it at
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html
Solve for the unknown distance, r. Show your work if you need additional assistance.