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Obtain an expression for the magnetic field at a point due to an infinitely long thin conductor or wire by applying Ampere's circuital law. |
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Answer» Solution :LET I be the current in the wire PQ. Let P be a point at a PERPENDICULAR distance r from the wire. Let dI be the element of length of the closed path. The direction of the magnetic FIELD will be tangential to the point P on the element. APPLYING Ampere's circuital law, we have `""ointvec(B).dvec(l)=mu_(0)I` i.e., `""ointBdlcos0^(@)=mu_(@)I, ""theta=0^(@)` between tangent drawn at P to the element of length dl and `vec(B)`. Thus `""Bointdl=mu_(@)I` or `""B=(mu_(0)I)/(ointdl)=(mu_(0)I)/(2pir)` Thus `""B propto 1/r` Note : B along the axis of the wire = 0 
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