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A magentic flux through a statinary loop with a resistance `R` varies during the tiem interval `tau` as `Phi = at (tau - t)`. Find the amount of heat generated in the loop during that time. The inductance of the loop is to be neglected. |
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Answer» The amount of heat generated in the loop during a small time interval `dl`, `d Q = xi^(2)//R dt`, but `xi = - (d Phi)/(dt) = 2 at-a tau`, So, `d Q = ((2 at - a tau)^(2))/(R) dt` and hence, the amoung of heat, generated in the loop during the time interval 0 to `tau`. `Q = int_(0)^(tau) ((2at - a tau)^(2))/(R) dt = (1)/(3) (a^(2) tau^(3))/(R)` |
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