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Explain how Biot-Savart's law enables one to express the Ampere's circuital law in the integral form , viz., oint vecB .vec(dl) = mu_0 I where I is the total current passing through the surface. |
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Answer» Solution :Let us consider an infinitely long straight WIRE in which a current I is flowing. To find magnetic field at a point P situated at a normal distance R from the wire consider a circular loop of RADIUS R AROUND the wire and in a plane perpendicular to the wire so that magnetic field `vecB` is tangential to the circumerence of the circle. For such a case `oint vecB. vec(dl) = int B dl = B int dl = B . 2 pi R` But as per Biot-Savart.s law we know that magnetic field B at a normal distance R from a long long straight current carrying wire is `B = (mu_0 I)/(2 pi R)` Hence, we get : `oint vecB . vec(dl) = ((mu_0 I)/(2 pi R)) 2 pi R = mu_0 I`. which is the INTEGRAL form of Ampere.s circuital law. 
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