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In a certainregion of the inertial reference framethere ismagneticfield with induction B rotatingwith angluar velocity omega. Findgrad xx E in thisregionas a function of vectorsomega and B |
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Answer» Solution :A ROTATING MAGNETICFIELD can be REPRESENTED by, `B_(x) = B_(0) cos omega t, B_(y) = B_(0) sin omega t` and`B_(x) = B_(zo)` Thencurl, `vec(E) = - (DEL vec(B))/(del t)`, So,`-(Curl vec(E))_(x) = -omega B_(0) sin omega t = -omega B_(y)` `-(Curl vec(E))_(y) = omega B_(0) cos omega t = omega B_(x)`, and `-(Curl vec(E))_(x) = 0` HENCE, Curl `vec(E) = -vec(omega) xx vec(B)`, where, `vec(omega) = vec(e_(3))omega`. |
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