What is the name associated with the equation $ \varnothing \vec E . \vec {dt} = - { d \varnothing \beta \over dt } $
The given equation $\oint \vec{E} \cdot d\vec{t} = -\frac{d\Phi_B}{dt}$ is Faraday's law of electromagnetic induction. This law states that a changing magnetic field within a closed loop induces an electromotive force (EMF) in the loop. The negative sign indicates the direction of the induced EMF, which opposes the change in magnetic flux, as per Lenz's law.