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In a certain region of the inertial reference frame there is magnetic field with induction `B` rotating with angluar velocity `omega`. Find `grad xx E` in this region as a function of vectors `omega` and `B` |
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Answer» A rotating magnetic field can be represented by, `B_(x) = B_(0) cos omega t, B_(y) = B_(0) sin omega t` and `B_(x) = B_(zo)` Then curl, `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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