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An infinitely long thin wire carrying a uniform linear static charge density lambda is placed along the z - axis. The wire is set into motion along its length with a uniform velocity V=v hat(k)_(z). Calculate the pointing vector S=(1)/(mu_(0))(vec(E )xx vec(B)). |
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Answer» Solution :Electric field produced due to infinitely long CHARGED WIRE, `vec(E )=(lambda)/(2pi in_(0)a)HAT(j) ""` …(1)  a = radius of cylinderical Gaussian surface AROUND wire. Magnetic field at .a. distance from current carrying conductor, `vec(B)=(mu_(0)I)/(2pi a)hat(i)` but `I=(Q)/(t)=(lambda L)/(t)=lambda v [because Q=lambda L " and " (L)/(t)=v]` Here L = length `therefore vec(B)=(mu_(0)lambda v)/(2pi a) ""`...(2) Now pointing vector, `S=(1)/(mu_(0))(vec(E )xx vec(B))` `therefore S=(1)/(mu_(0))[(lambda)/(2pi a)hat(j)xx(mu_(0)lambda v)/(2pi a)hat(i)]` `=(1)/(mu_(0))((lambda)/(2pi a)xx(mu_(0)lambda v)/(2pi a))(hat(j)xx hat(i))` `=(lambda^(2)v)/(4pi^(2)in_(0)a^(2))(-hat(k)) ""[because hat(j)xx hat(i)=-hat(k)]` `therefore S=-(lambda^(2)v)/(4pi^(2)in_(0)a^(2))hat(k)` |
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