The magnitude of the magnetic field 8.0 cm from a straight wire carrying a current of 6.0 A is
A) 3.0 ƒÎ �~ T.
B) 1.5 �~ T.
C) 1.5 �~ T.
D) 3.0 �~ T.
E) 3.0 �~ T.
dggds
I don’t understand
To find the magnitude of the magnetic field at a distance of 8.0 cm from a straight wire carrying a current of 6.0 A, we can use Ampere's law. Ampere's law states that the magnetic field around a wire is directly proportional to the current and inversely proportional to the distance from the wire.
The formula for the magnetic field due to a straight wire is given by:
B = (µ₀ * I) / (2π * r)
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.
Plugging in the given values:
B = (4π * 10^-7 T*m/A * 6.0 A) / (2π * 0.08 m)
Simplifying the expression:
B = (2 * 10^-6 T) / (0.08 m)
B = 0.025 T
So, the magnitude of the magnetic field 8.0 cm from the wire carrying a current of 6.0 A is 0.025 T.
Therefore, the correct answer is:
B) 0.025 T.
To find the magnitude of the magnetic field, we can use the formula given by the Biot-Savart law:
B = (μ₀ * I) / (2π * r)
where B is the magnetic field, μ₀ is the magnetic constant (≈ 4π x 10^-7 T m/A), I is the current, and r is the distance from the wire.
Plugging in the values into the formula:
B = (4π x 10^-7 T m/A * 6.0 A) / (2π * 0.08 m)
Simplifying the equation:
B = (24π x 10^-7 T m) / (2π * 0.08 m)
The π in the numerator and denominator cancel out:
B = (24 x 10^-7 T m) / (2 * 0.08 m)
Simplifying further:
B = 3 x 10^-7 T
So, the magnitude of the magnetic field 8.0 cm from the wire carrying a current of 6.0 A is 3.0 x 10^-7 T.
Therefore, the correct answer is option D) 3.0 x 10^-7 T.