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Using Eqs. Demonstrate that if in the intertial reference frame Kthere is only electricor only magnetic field. In any other interial frame K' both electric and magneticfiedlswill coxist simutaneously, with E' _|_ B'. |
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Answer» Solution :Suppose, thereis only electric fied `vec(E)`, in `K`. THENIN `K'`, consideringnonrelativistic velocity `vec(v), vec(E') = vec(E), vec(B) = (vec(v) XX vec(E))/(c^(2))`, So, `vec(E') vec(B') = 0` In the relatiistic case, `{:(vec(E')_(||)=vec(E)_(||)),(E'_(bot)=(vec(E_(bot)))/(sqrt(1-v^(2)//c^(2)))):}}{:(vecB'_(||)=vec(B)_(||)=0),(vec(B')_(bot)=(-vec(v)xxvec(E)//c^(2))/(sqrt(1-v^(2)//c^(2)))):}` Now,`vec(E').vec(B') = vec(E'_(|\|)). vec(B'_(|\|)) + vec(E'_(_|_)). vec(B'_(_|_)) = 0`, since `E'_(_|_).'B'_(_|_) =-vec(E_(_|_)). (vec(v) xx vec(E))//(1 - v^(2)//c^(2)) = vec(E_(_|_)).(vec(v) xx vec(E_(_|_))//(1 - (v^(2))/(c^(2))) = 0'` |
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