# 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 = (μ_{0} N I a^{2}) / [2 (a^{2} + x^{2})^{3/2}]

we know, μ_{0} = 4π x 10^{-7}

Putting all values:

=> Magnetic field B = [ 4π x 10^{-7}x 1 x 5 x 0.05^{2}] / [ 2 (0.05^{2}+ 0.1^{2})^{3/2}]

B= 57.2 x 10^{-7}T