1. Tardigrade
  2. Question
  3. Physics
  4. The magnetic flux through a stationary loop with a resistance R varies during interval of time T as φ=a t(T- t). If the heat generated during this time, neglecting the inductance of the loop, is (a2 T3/p R), then find p.

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Q. The magnetic flux through a stationary loop with a resistance $R$ varies during interval of time $T$ as $\phi=a t(T-$ $t)$. If the heat generated during this time, neglecting the inductance of the loop, is $\frac{a^{2} T^{3}}{p R}$, then find $p$.

Electromagnetic Induction

Solution:

$\phi=a t(T-t) ; \quad|\varepsilon|=\frac{d \phi}{a t}=a T-2 a t$
$d H=\varepsilon I d t=\frac{(a T-2 a t)(a T-2 a t)}{R} d t$
$\int\limits_{0}^{H} d H=\int\limits_{0}^{T} \frac{(a T-2 a t)^{2}}{R} d t$
$H=\frac{a^{2} T^{3}}{3 R}$