A wire carries a current I. At a distance of 6mm from the wire, the magnetic field strength is 0.004T. find the magnitude of current I.
B=mu*current/(2PI*distance)
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html
To find the magnitude of the current I, we can use Ampere's law, which relates the magnetic field around a closed loop to the current passing through the loop.
Ampere's law states that the line integral of the magnetic field B around a closed loop is equal to the product of the current I passing through the loop and the permeability of free space μ₀.
Mathematically, Ampere's law can be written as:
∮ B · dl = μ₀ I
where ∮ B · dl represents the line integral of the magnetic field B along the closed loop and μ₀ is the permeability of free space (μ₀ = 4π × 10⁻⁷ T⋅m/A).
In your case, the wire carries a current I and the magnetic field strength at a distance of 6 mm from the wire is given as 0.004 T.
Let's assume that the magnetic field strength is constant around a circular loop of radius r, which is at a distance of 6 mm = 0.006 m from the wire.
Using Ampere's law, we can write the equation as:
B * 2πr = μ₀ I
Substituting the given values into the equation:
0.004 T * 2π * 0.006 m = 4π × 10⁻⁷ T⋅m/A * I
0.024π = 4π × 10⁻⁷ * I
Simplifying the equation:
I = (0.024π) / (4π × 10⁻⁷)
I = 6 × 10⁴ A
Therefore, the magnitude of the current I is 6 × 10⁴ Amperes.