stationary electron in a time varying field A moving electron in a stationary magnetic field will experience magnetic Lorentz force given by $q(\vec v\times\vec B)$.
But will a stationary electron placed in a time varying magnetic field experience the magnetic Lorentz force? If yes then what is the formula of the force?
 A: $\newcommand{\curl}[1]{\nabla \times #1}$
$\newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}}$
Yes. Stationary electron does experience a Electric Force in a time varying Magnetic Field.
In a time Varying Magnetic Field, Electric Field will be produced,
$$ \curl \vec E = - \pdv{B}{t} $$
So, this Electric Field produces the force on the Stationary electron.
And Force by Electric Field is Given by,
$$ \vec F = q \vec E $$
A: 
let $\overrightarrow{B(t)}$ be the time varying magnetic field
  $\newcommand{\dv}[2]{\frac{\mathrm{d} #1}{\mathrm{d}#2}}$
  lorentz force DOES apply when there is some  magnetic field $$F_M = q \overrightarrow{v}\times\overrightarrow{B}$$

now let's consider the magnetic field is created by a coil and the electron is at some point in the coil. now using faraday's law , electric field $\overrightarrow{E}$ at a point on the plane of the coil at a distance $\overrightarrow{R}$ from the center will be
$$\mathcal{E} = -\dv{\phi_B}{t}$$
$$ER = -\pi R^2 \dv{B}{t}$$$$E=-\pi R \dv{B }{t}$$$$\overrightarrow{E}=\overrightarrow{R}\times\overrightarrow{A} \pi \dv{B}{t}$$ where $\overrightarrow{A}$ is a unit vector perpendicular to the plane of coil.
so force due to this electric field also acts on the body
A: We can use the potentials to express the external electromagnetic field on general form:
$$
\mathbf E = -\nabla\phi - \frac{\partial\mathbf A}{\partial t}\quad\mbox{ and }\quad
\mathbf B = \nabla\times\mathbf A
$$
Note the we have $\mathbf E = \mathbf E(\mathbf r, t)$ and same for $\mathbf B$. This is quite general. So they are time varying and space-varying. This gives a Lorentz Force of:
$$
\frac{\mathbf{dp}}{dt} = 
\mathbf F = q\left(\mathbf E + \mathbf v\times\mathbf B\right) = 
q\left(-\nabla\phi - \frac{\partial\mathbf A}{\partial t}
- \mathbf v\times\nabla\times\mathbf A
\right)
$$
Using vector relations and reorganizing a little bit, we have the equations of motion:
$$
\frac{d}{dt}\left(\mathbf p + q\mathbf A\right) = 
\nabla\left(q\mathbf v\cdot\mathbf A - q\phi \right)
$$
If you are curious you can put it in a computer program and an stationary electron to see what happens. But yes, your classical stationary electron will experience Lorentz Force. Please note here its only valid for non-radiating electron. But works in some cases as good approximation. In the case of a radiating electron, Lorentz force needs is not adequate and needs a correction.
