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A circular coil of radius R carries a curretn. Find an expression for the magnetic field due to this coil at its centre. Also find the direction of field. |
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Answer» Solution :Consider a circular loop of radius R carrying a current I in clockwise direction. The loop may be considered to be divided into a LARGE number of current elements. Consider one such current element of length dl as shown in fig. Magnetic field at the centre POINT O of the loop due to this element, as per Bio-Sarvart.s law is `DB = (mu_0)/(4pi) cdot (I dl sin 90^(@))/(R^2) = (mu_0)/(4 pi) cdot (I dl)/(R^2) "[ Here " = THETA = 90^(@)]` The total magnetic field due to current loop `B = (mu_0)/(4 pi) cdot (I)/(R^2) sum dl = (mu_0 I)/(4 pi R^2) cdot (2 pi R) = (mu_0 I)/(2 R)[ :. sum dl = 2 pi R]` If instead of a single loop we have a circular coil of N turns, then `B = (mu_0 N I)/(2 R)` The magnetic field is directed perpendicular to the plane of paper directed inward. 
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