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In a uniform magneitc field of induced B a wire in the form of a semicircle of radius r rotates about the diameter of hte circle with an angular frequency `omega`. The axis of rotation is perpendicular to hte field. If the total resistance of hte circuit is R, the mean power generated per period of rotation isA. `(B pi r^(2) omega)/(2R)`B. `((B pi r^(2) omega)^(2))/(8R)`C. `((B pi r omega)^(2))/(2R)`D. `((B pi r omega H_(2))^(2))/(8R)` |
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Answer» Correct Answer - B `phi = BA cos theta` `= B((pi r^(2))/(2)) cos omega t` `E = -(d)/(dt) phi = (B pi r^(2))/(2) omega sin omega t` `P = (E^(2))/(R ) = (B^(2) pi^(2)r^(4)omega^(2))/(4R) sin^(2) omega t` But `lt sin^(2) omega t gt (1)/(2)` `:. lt P gt =((B pi r^(2) omega)^(2))/(8 R)` |
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