InterviewSolution
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InterviewSolution
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A direct current of density `j` flows along a round unifrom staright wire with cross-section radius `R`. Find the magnectic induction vector of this current at the point whose position relative to the axis of the wire is defined by a radius vector `r`. The magentic permeabilility is assumed to be equla to unity thoughhout all the space. |
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Answer» By circulation theorem inside the conductor `B_(varphi) 2pi r = mu_(0) j_(x) pi r^(2)`, or `B_(varphi) = mu_(0) j_(x) r//2` i.e., `vec(B) = (1)/(2) mu_(0) vec(j) xx vec(r)` Similarly outside the conductor, `B_(varphi) 2pi r = mu_(0) j_(x) pi R^(2)` or, `B_(varphi) = (1)/(2) mu_(0)j_(x) (R^(2))/(r)` So, `vec(B) = (1)/(2) mu_(0) (vec(j) xx vec(r)) (R^(2))/(r^(2))` |
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