The magnetic flux linked with a coil (in Wb) is given by the equation $\phi = 5t^2 + 3t + 60$. The magnitude o

Question

The magnetic flux linked with a coil (in Wb) is given by the equation $\phi = 5t^2 + 3t + 60$. The magnitude of induced emf in the coil at $t = 4$ s will be:

Accepted Answer

1.  **Faraday's Law:** The magnitude of the induced electromotive force (emf) $\varepsilon$ in a circuit is equal to the time rate of change of magnetic flux $\phi$ through the circuit. Mathematically, $|\varepsilon| = \left| \frac{d\phi}{dt} ight|$ .
2.  **Differentiation:** We are given the magnetic flux function $\phi = 5t^2 + 3t + 60$. To find the induced emf, we differentiate this function with respect to time $t$:
    $\frac{d\phi}{dt} = \frac{d}{dt}(5t^2 + 3t + 60) = 10t + 3$.
3.  **Calculation:** We need to find the magnitude of the induced emf at $t = 4$ seconds. Substituting $t = 4$ into the derivative:
    $|\varepsilon| = 10(4) + 3$
    $|\varepsilon| = 40 + 3 = 43 	ext{ V}$.

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