The power dissipated in the loop can be calculated using the formula:
\[ P = I^2 R \]
Where \(I\) is the induced current and \(R\) is the resistance.
The magnetic flux change through the loop is given by:
\[ \frac{dB}{dt} = 10^{-7} \, \text{T/s} \]
Using Faraday’s Law, the induced emf in the loop is:
\[ \mathcal{E} = -N \frac{d\Phi}{dt} \]
Now, calculate the induced current \(I\):
\[ I = \frac{\mathcal{E}}{R} \]
Substituting the values, we find the power dissipated:
\[ P = 2.16 \times 10^{-9} \, \text{W} \]
\[ P = 216 \times 10^{-9} \, \text{W} \]
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: