# Energy loss and power over one period?

Let's say we have a ferrite core inductor connected to an AC sinusoidal source with period $T$. Thus, we have voltage $u(t)$ across the inductor and current $i(t)$ through the inductor.
How can we find the equations which describe the power and energy loss due to hysteresis over one period?

We know that power at any point in time is given by: $p(t)=u(t)\cdot i(t)$ and the energy loss over one period is: $$W(T)=\int_T{p(t)dt}$$ But, where do we go from there?

• If we take arbitrary dimensions (let's say the core is shaped like a cylinder and has a radius $r$) and there are $N$ turns around the core. The length of the inductor is $l$ and the relative permeability of material is 500, how do we go from here? – A6EE Jan 18 '18 at 18:49