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State Ampere's circuital law . Using it, derive the expression for magnetic field at a point due to a long current carrying conductor . |
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Answer» Solution :Statement : The LINE integral of magnetic field around any closed path in FREE SPACE is equal to `mu_0` times the net current enclosed by that path. i.e., `ointvecB.dvecI=mu_0I`  CONSIDER a infinitelylong CONDUCTOR carrying a current .Let `I_e` be the current enclosed by the loop and L be the length of the loop for which .B. is tangential , then the amperes circuital law `oint vecB.dvecI=mu_0I` becomes `BL=mu_0I` If we assume a straight conductor and the boundary of the surface surrounding the conductor as a circle , then length of the boundary is the circumference , `2pir` , where .r. is the radius of the circle . Then B. `2pir=mu_0I` `therefore B=(mu_0I)/(2pir)` |
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