There is a change in flux produced by the changing magnetic field which is given by

where  is the cross sectional area of the coil,  is the change in magnetic field, and  is the angle of the field lines relative to the normal of the cross section of the coil.

In this case the magnet is perpendicular to the cross section of the coil and so

The change in magnetic field is just the final given value minus the intial value. Faraday's Law says that an emf will be generated by a change in flux,

where  is the number of turns in the coil. Plugging in the change in flux gives

The change in time is just  since we can start our clock at zero. The current can be found using Ohm's Law where

Write the formula for inductance and substitute the givens. The length of the solenoid has no effect in this problem.

The relationship between the number of turns for the primary coil and secondary coil in a transformer ( and  respectively) to the relative potentials is

Solving for ,

Magnetism is caused by electrons in a material aligning and causing an aggregate magnetic field that can exert influence over other things. The magnetic strength is limited by random fluctuations in the electrons, making them no longer aligned. If the magnet were to be cooled, the electrons would have less kinetic energy, and would be less likely to have random fluctuations. This would make the strength increase.

All of the other things would make the strength of a magnet decrease. Striking it would impart kinetic energy, and would momentarily vibrate the electrons. Likewise, heating it would make the electrons vibrate more.

In this question, we're told that the velocity filter is able to detect the speed of a particle when the magnetic force and electric force are equal to each other. In order to determine when the particle's velocity will be the greatest, we'll need to keep in mind the equations for both the electric force and magnetic force:

Next, we'll need to set them equal to each other:

Then, we can isolate the velocity term:

Based on this equation, we see that if we want to increase the particle's velocity, we'll need to increase the electric field. Increasing the particle's charge will have no effect on the particle's velocity, and increasing the magnetic field will actually decrease the particle's velocity.

The magnetic field around permanent magnets is caused by the alignment of the material's electrons, which no longer average out to a net field of zero and instead combine to form a greater field. If the electrons come out of alignment, then the field wanes or stops altogether. Additionally, the random vibrations of the electrons inhibits the effectiveness of the field. Therefore, if you were to apply energy to a magnet, it would be less effective because the electrons would have greater random motion. Heating the magnet applies thermal energy to it, and dropping it applies kinetic energy to it, which means neither of them would be the right answer. When you cool a magnet, you are removing some of the energy it has, making the electrons have less random motion.

A diamagnet is a material that, when it is exposed to a magnetic field, produces a magnetic field in the opposite direction as the external field, which leaves an overall lesser field.