# Magnetic flux density compard to other definition of flux

With regards to flux i have always assumed it was defined as $$(1) Something/m^2s$$ For instance $$Luminosity/(4\pi r^2)$$ Is an example of radiation flux.

Why then is faradys law often cited as the rate of change of magnetic flux is equal in magnitude to the induced emf $$\frac{d\phi}{dt} =\epsilon$$

where $$\phi =BA$$ So how can we call $$\phi$$ to be a flux as dimensionally it is not of the same form as (1).

It depends on it's a flux of what. Usually flux is defined for a vector field. It's obviously so for $$\phi(\vec B)$$. As to luminosity it too is a vector field: the current density of energy - dimensionally energy per unit area and time. But it also has a direction, characterizing it as a vector.