Question

If the magnetic flux through a coil is given by $\Phi = 5t^2 + 3t + 2$ what is the induced EMF at t = 2s?

Answer 1

23 V

Answer 2

Magnetic flux $\Phi = 5t^2 + 3t + 2$. Induced EMF $\mathcal{E}$ is given by the rate of change of magnetic flux. Following the convention of the similar question, we use $\mathcal{E} = \frac{d\Phi}{dt}$. $\mathcal{E} = \frac{d}{dt}(5t^2 + 3t + 2)$ $\mathcal{E} = 10t + 3$ At $t = 2$s, substitute $t=2$: $\mathcal{E}\Big|_{t=2} = 10(2) + 3$ $\mathcal{E}\Big|_{t=2} = 20 + 3$ $\mathcal{E}\Big|_{t=2} = 23$ V