Calculate the magnitude of the magnetic field……………?

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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 Biot-Savart 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 semi-circle, 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 right-hand 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…

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