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Numericals · Q22

Q.A wire loop of the form shown in the figure carries a current I. Obtain the magnitude and direction of the magnetic field at P. (Given a formula for the contribution of one segment, 'segment II', of the loop, in terms of μ0\mu_0, I and R.) [The printed answer for this item is a compound expression combining two different radii/segment contributions -- the exact shape of the loop (how many straight and curved segments, their radii, and P's position relative to them) is shown only in the source figure and is not recoverable from the extracted text.]

Maharashtra Board Std 12 Physics Magnetic Fields due to Electric Current: current-carrying wire loop of a 270 degree arc of radius R and a straight segment, magnetic field at centre P
Figure
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Concept understanding — Magnetic Field at the Centre of a Circular Current Loop

Applying the Biot-Savart law to a circular arc of wire exploits a special geometric fact unique to circles: every current element along the arc is always exactly perpendicular to the radius vector drawn to the centre, and every element is the same fixed distance from the centre. This simplifies the Biot-Savart integral for the field at the centre O of an arc of radius r subtending angle θ\theta (in radians) to B=μ04πIrθB=\dfrac{\mu_0}{4\pi}\dfrac{I}{r}\theta. …

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