We want to calculate the magnetic field at the point P, due to the current loop

Question

We want to calculate the magnetic field at the point P, due to the current loop shown in the figure. The radius of the wire is R, and the wire carries a current I. What is the magnitude of the magnetic field, dB vector, due to the ONE element ds vector shown in the figure? Express your result in terms of the knowns I, R, ds. Note that ds vector and r are perpendicular so ||ds vector times r|| = ds What is the direction of the field dB vector? Using the fact that all elements of the wire produce a magnetic field in the same direction at point P, write an expression, in the form of an integral, for the magnitude of the total magnetic field at P due to all of the elements that make-up the wire. Evaluate the integral, it is easy to do so.

Explanation / Answer

a) Into the page

b) dB = (mue/(4*pi))*(I*ds*sin(90)/R^2)

= (mue/(4*pi))*(I*ds/R^2)

Total magnetic field at the center, B = integral dB

B = integral (mue/(4*pi))*(I*ds/R^2)

c) B = integral (mue/(4*pi))*(I*ds/R^2)

= (mue/(4*pi))*(I/R^2) intgeral dS

= (mue/(4*pi))*(I/R^2)*(2*pi*R)

= mue*I/(2*R)

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