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State the Biot-Savart law for the magnetic field due to a current-carrying element. Use this law to obtain a formula for magnetic field at the center of a circular loop of radius a carrying a, steady current I. 

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Biot-Savart Law 

It states that the magnetic field strength (dB) produced due to a current element (of current I and length dl) at a point having position vector r relative to current element is 

where μ0 is permeability of free space. Its value is μ0 = 4π x 10 -7 Wb/A-m. The magnitude of magnetic field is

where q is the angle between current element I vector dl and position vector r. The direction of magnetic field vector dB is perpendicular to the plane containing I vector dl and vector r. 

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