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Using Maxwell's equacations. Show that (a)a time dependentmagneticfield cannotexistwithoutan electric field, (b) a unifromelectric fieldcannotexist in thepresenceofa time-dependencemagneticfield, (c)insidean emptycavitya unifromelectric(or magnetic ) fieldcan betime-dependent. |
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Answer» SOLUTION :(a) If `vec(B) = vec(B) (t)`, then, CURL `vec(E) = (-del vec(B))/(del t) != 0`. so, `vec(E)` cannot vanish. (b) Here also, curl `vec(E) != 0`, so `vec(E)` cannot be uniform. (c) Suppose for instance, `vec(E) = vec(a) f(t)` where `vec(a)` si spatially and temporally FIXEDVECTOR. Then `- (del vec(B))/(d t) = curl vec(E) = 0`. Generally speakingthis contradicts the otherequactioncurl `vec(H) = (del vec(D))/(del t) != 0` for in thiscase the left hand SIDE is TIME independentbut `RHS`dependson time. The onlyexception is when`f(t)` is linearfunction. Thena unifromfield `vec(E)`can be timedependent. |
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