Calculate the magnitude of the magnetic field at point P due to the current in the semicircular section of wire shown in the figure . (Hint: Does the current in the long, straight section of the wire produce any field at P?)Express your answer in terms of the variables I, R and appropriate constants.
B) Find the direction of the magnetic field at point P: into the page or out of the page?
2 Answers

(A) Integrate around the curve, from 0 to π radians, to sum up the total at P. Ignore the straight part, since obviously that doesn’t contribute when the radial distance from the straight part is zero.
I’ll use the BiotSavart law instead of Ampere’s law, since there’s isn’t symmetry to simplify the line integral.
dB = (µ0/4π) I dsxR / R^3 where x means cross product
ds is the wire element vector pointing tangent to the wire.
So I ds is a differential current element.
r is a vector pointing toward P.
Since s and r are perpendicular all along the semicircle, the cross product is just ds * r.
We rewrite dB as
(µ0/4π) I ds / R²
I and R are constant. So we’re really just integrating ds over the wire curve from 0 to π.
So all we’re finding by integrating is the length of the wire that’s curved. That’s just πR.
So B = µ0 I / 4R
(B) Using the righthand rule, it should be pretty obvious.

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Calculate the magnitude of the magnetic field……………?
Calculate the magnitude of the magnetic field at point P due to the current in the semicircular section of wire shown in the figure . (Hint: Does the current in the long, straight section of the wire produce any field at P?)Express your answer in terms of the variables I, R and appropriate…