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.

Magnetic fields do not affect charges that are moving parallel to them. 

Thus, the magnetic force will be at a maximum when moving perpendicular to the field, and at zero when moving parallel to the field.

The centripetal force will need to be equal to the magnetic force.

Solving for

Converting:

Plugging in values: