electromagnetism - Time varying magnetic field, yielding two effects of induction?

$B_s$ is nonuniform, and it's generated from a movable source(e.g magnet or electromagnet).

A rectangular loop of area $A$ is stationary.

The variation of flux for this case is caused from the following:

1. Spatial movement of $B_s$.


2. Strength variation $B_s$ of due to (1).

How can I quantitatively formulate $\varepsilon_{induced}$ here?

I could assume that:

$$\varepsilon_{induced} =\oint \vec{E} \cdot \vec{dl} = -\frac{\delta \Phi}{\delta t}$$

to:

$$\varepsilon_{induced} =\oint \vec{E} \cdot \vec{dl} = -\int \frac{\delta B_s}{\delta t} \cdot \vec{da}$$

But how can I factor in the effects of 1&2 to $\delta B_s$?

From my textbook,the examples brought up had the effects(1&2) mutually exclusive, but for this case both add to $\varepsilon_{induced}$