Question

what is the equation for magnetic induction?

Answer 1

what is the equation for magnetic induction?

The most widespread version of Faraday's law states:

The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit:

$$\mathcal{E} = - \frac {d \Phi_{B}}{d t}$$

where $\mathcal{E}$ is electromotive force acting along an arbitrarily chosen path,

$$\Phi_{B} = \iint_{S} \vec{B} \cdot d \vec{S},$$

-- magnetic flux through the surface stretched on this path.

For example, for a tightly wound coil of wire, composed of $N$ identical loops, each with the same $\Phi_B$, Faraday's law of induction states that

$$\mathcal{E} = - N \frac {d \Phi_{B}}{d t} = - \frac {d \Psi}{d t}$$

where $N$ is the number of turns of wire, $\Phi_B$ is the magnetic flux in webers through a single loop and $\Psi$ is the flux linkage of a coil.