The force experienced by a charged particle in a magnetic field is 

This means that when a charge particle is moving perpendicular to the field, due to the cross-product, it experiences the most amount of force (because  is equal to , and theta equals  when it's perpendicular). This means that the charged particle will experience no force due to the magnetic field when it's parallel. We know there will be no force on the particle, and we also know that uncharged particles experience no force in magnetic fields, but we can't say for certain the particle has no net charge, only being told that it's moving parallel to the field.

The rod acts as a battery due to its motion in the magnetic field: . Because there is a closed circuit, this results in current flow:

In this simple circuit, the current is the same everywhere, so the same current flows through the rod. Because of this current, the rod feels a force:

By the right-hand rule, this magnetic force is directed to the left, so the external force must be directed to the right. It is interesting to note that the power dissipated in the resistor:

 is the same as the power provided by the outside force:

The universe conspires to conserve energy.

This question is presenting us with a scenario in which a charged particle is traveling with a certain velocity through a magnetic field. In this situation, we're being asked to determine what the force experienced by this particle is.

To solve this question, we'll need to determine what kind of force this particle is likely to experience. Since we're told that the particle is traveling in a magnetic field, it would make sense that this particle is going to be affected by a magnetic force. Thus, we'll need to use the equation for magnetic force.

Moreover, since we're told in the question stem that this particle is traveling perpendicularly to the magnetic field, we know that  and thus . This helps reduce the equation down.

Now, all we need to do is plug in the values given to us in order to calculate the resulting force.

Charged particles only experience a magnetic force when some component of their velocity is perpendicular to the magnetic field. Here, the velocity is parallel to the magnetic field so the particle does not experience a force. 

Use the magnetic force equation:

Plug in known values and solve for 

Using the right hand rule for a current carrying wire shows that the magnetic field is pointing out of the screen. Using the right hand rule for magnetic force on a negatively charged particle shows the force acting downward.

In this question, we're asked to determine which answer choice falsely represents a necessary condition for a magnetic force to act on a particle.

To answer this, it is useful to look at the equation for magnetic force.

What this equation shows is that the magnetic force on a particle is dependent upon that particle's charge, its velocity, and on the strength of the magnetic field. Already we can rule out a few of the answer choices.

Additionally, this equation also shows that  cannot be equal to zero. What this means is that the particle's direction of motion cannot be along the magnetic field lines. In other words, the particle cannot be travelling in a direction that is parallel or antiparallel with the magnetic field.

Lastly, we can see that no where in the above equation is there a variable for the size of the particle. Thus, size is not a requirement for a particle to experience a magnetic force.

Using

Where

 is the charge limited to traveling in a single dimension

 is the free charge

 is the distance between the charges

 is the velocity of the first charge

 is the velocity of the second charge

 is the value of the first charge

 is the value of the second charge

 and  are equivalent as the charges are running parallel to each other

Combining equations:

Solving for 

Plugging in values:

Finding the magnetic field at the location of the proton.

Converting  to  and plugging in values

Using

Since the electron is stationary, there will be no magnetic force, as magnetic force requires the particle to be both charged and to be moving.