Calculate the magnetic field at point P located on the axis at a distance of 10 cm from the center of a circular wire of radius 5 cm carrying a current of 5 A.

Problem statement: Calculate the magnetic field at point P located on the axis at a distance of 10 cm from the center of a circular wire of radius 5 cm carrying a current of 5 A.

Solution:

Given:
radius of circular wire: a = 5 cm = 0.05 m
current I = 5 A
On the axis, the distance between the center of the circular wire and the point P: x = 10 cm = 0.1 m
Number of turns N = 1 (as it is not mentioned in the question, we are assuming it to be 1)
Magnetic field B = ?

B = (μ₀ N I a²) / [2 (a² + x²)^3/2]

we know, μ₀ = 4π x 10^-7

Putting all values:
=> Magnetic field B = [ 4π x 10^-7 x 1 x 5 x 0.05²] / [ 2 (0.05² + 0.1²)^3/2]
B= 57.2 x 10^-7 T