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In an interial reference frameK there are twouniformmutulaly perpendicularfields, an electricfieldof strengthE = 40 kV//m anda magnetic fleid induction B = 0.20 mT. Find theelectricstrengthE' (or the magnetic induction B') in the referenceframeK' where onlyone field, electricor magnetic, is observed. |
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Answer» SOLUTION :In this case, `vec(E).vec(B) = 0`, as the FIELDS are mutually perpendicular.Also, `E^(2) - c^(2) B^(2) = -20 xx 10^(8) ((V)/(m))^(2)` is `-ve`. Thus, we can finda frame, in which `E' = 0`, and `B' = (1)/(c) sqrt(c^(2) B^(2) - E^(2)) = B sqrt(1 - (E^(2))/(c^(2) B^(2))) = 0.20 sqrt(1 - ((4 xx 10^(4))/(3xx10^(8)xx2xx10^(-4)))^(2)) = 0.15 mT` |
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