Moving a magnet inside a coil of wire will induce a voltage in the coil. How is the voltage in the coil increased?
by moving the magnet inside the coil of wire more slowly
by moving the magnet inside the coil of wire more rapidly
by holding the magnet absolutely still
by moving the coil of wire slowly, and keeping the magnet stationary
The voltage induced in a coil of wire is directly related to the rate at which the magnetic field through the coil changes. To increase the voltage in the coil, you need to increase this rate of change.
Moving the magnet inside the coil of wire more slowly will indeed increase the duration of time over which the magnetic field changes, effectively increasing the rate of change. Therefore, moving the magnet inside the coil of wire more slowly will increase the voltage induced in the coil.
On the other hand, moving the magnet inside the coil of wire more rapidly will decrease the duration of time over which the magnetic field changes. This will result in a lower rate of change and therefore a lower induced voltage.
Holding the magnet absolutely still will not cause any change in the magnetic field through the coil, and thus, no voltage will be induced.
Lastly, moving the coil of wire slowly while keeping the magnet stationary will not result in any change in the magnetic field passing through the coil. Since the rate of change is zero, there will be no induced voltage.
In summary, to increase the voltage induced in the coil, you should move the magnet inside the coil of wire more slowly.
The voltage induced in a coil of wire is increased by moving the magnet inside the coil more rapidly. The rate at which the magnetic field lines are cut by the coil determines the magnitude of the induced voltage. Moving the magnet rapidly increases the rate at which the field lines are cut, thus increasing the induced voltage.
Well, you could use Maxwell's equations, but it might be easier to make a common sense guess.
If moving the magnet makes a voltage, then it is likely that moving it faster will make a bigger voltage.