1 \begin{problem*}{23.7} % induction
2 An $N=30$ turn circular coil of radius $r = 4.00\U{cm}$ and resistance
3 $R = 1.00\Omega$ is placed in a magnetic field directed perpendicular
4 to the plane of the coil. The magnitude of the magnetic field varies
5 with time according to $B = 0.0100t + 0.0400t^2$, where $t$ is in
6 seconds and $B$ is in Tesla. Calculate the induced emf in the coil
11 The magnetic flux through the loop is
13 \Phi_B &= AB = N \cdot \pi r^2 \cdot B \\
14 \varepsilon &= - \frac{d\Phi_B}{dt} = - 30 \cdot \pi r^2 \cdot \frac{dB}{dt}
15 = -30 \cdot \pi (0.0400\U{m})^2 \cdot (0.100 + 0.800t)\U{T/s}
16 = \ans{61.8\U{mV}} \;.