I am taking some of the assumptions to keep the case ideal and simple to understand the first assumption I'm going to take is that the field lines originating from the magnet are parallel and equidistant from eachother that means the field strength is uniform in the direction in which the magnet is oriented at some instant because the magnet is rotating, secondly if the field strenght is constant (magnitude wise) then the distance from the magnet to the coil doesn't matter at all.
Since this is the case of rotating magnetic field then it's going to produce an Alternating Current no DC current let's understand how:-
As we know that
$\phi_B = \vec{B} • \vec{A}$
$\phi_B = ABcos \theta$
Since there are "$N$" turns in the solenoid the total Flux will also become "$N$" times so total Flux will come out to be:-
$N \phi_B = NABcos \theta$
Assigning $N \phi_B$ as $\phi_0$ So,
$\phi_0 = NABcos \theta$
By differentiating both side with time we will get
$-\frac{d (\phi_0)}{dt} = \frac{d(NABcos \theta)}{dt}$
Negative sign is because of:-
$E_0 = -\frac{d \phi}{dt}$
Since number of turns, magnetic field strength and area are constant all the time and due to the rotation of the magnetic field the angle between the field lines and the area vector is going to change so The final equation you are going to get is:-
$E_0 = NBAsin \theta • \frac{d \theta}{dt}$
Since $\frac{d \theta}{dt}$ is $\omega$ the equation will be
$E_0 = NBA \omega sin \theta$
Hence you got the equation for the induced EMF in the case of rotating magnet, and here when the the angle between the area vector and the field is 0 then no EMF will be induced, in the case if it's perpendicular then the induced EMF will be maximum and when the angle between them will be greater than $180°$ then the induced EMF will be negative or in other words if we can imagine a battery which is formed then it's orientation is going to change and you will get the current in the opposite direction as that of before.
And by dividing both the sides of the equation with the resistance of the wire then you can find the current as well, so there you go! 628