Magnetic Induction due to a Current-carrying Wire

To determine the magnetic induction or magnetic field strength at a perpendicular distance from a long straight wire carrying an electric current, we can use the formula given by Ampere's law. Ampere's law states that the magnetic field strength around a closed loop is directly proportional to the current passing through the loop.

The Formula
The formula to calculate the magnetic field strength (B) at a perpendicular distance (r) from a long straight wire carrying a current (I) is given by:

B = μ₀ * (I / 2πr)

Where:
B = magnetic field strength (in Tesla)
μ₀ = permeability of free space (4π × 10⁻⁷ T·m/A)
I = electric current (in Amperes)
r = perpendicular distance from the wire (in meters)
π = mathematical constant pi (approximately 3.14159)

Given Values
In this case, the electric current passing through the wire is 2 Amperes, and the perpendicular distance from the wire is 5 meters. We can substitute these values into the formula to calculate the magnetic induction.

Calculating the Magnetic Induction
Using the formula mentioned earlier:

B = (4π × 10⁻⁷ T·m/A) * (2 A / 2π * 5 m)
B = (4π × 10⁻⁷ T·m/A) * (1 A / 5 m)
B = 8π × 10⁻⁸ T/m

The Result
Therefore, the magnetic induction or magnetic field strength at a perpendicular distance of 5 meters from the wire carrying a current of 2 Amperes is approximately 8π × 10⁻⁸ Tesla per meter.

Explanation
- The formula used to calculate the magnetic induction is derived from Ampere's law, which relates the magnetic field strength to the current passing through a closed loop.
- The magnetic field strength decreases as the distance from the wire increases. This inverse relationship is due to the spreading out of the magnetic field lines as they move away from the wire.
- The value of μ₀ represents the permeability of free space, which is a constant value in physics.
- The formula also includes a factor of 2πr in the denominator to account for the circular path around the wire where the magnetic field is being measured.