When finding the direction of the force on a POSITIVELY charged particle due to a magnetic field, we can use the right hand rule. Holding your thumb perpendicular to the rest of your fingers (as if motioning to stop), orient your fingers parallel to the lines of the magnetic field, and your thumb with the velocity vector of the charge. For a positive charge, the force would be oriented directly out of the palm; HOWEVER, the charge of an electron is negative and therefore the force will be applied in the opposite direction. This would mean that the force would be coming directly out of the backside of your hand (in this case, towards the top of the page) using the right hand rule.

A charged particle's motion in a uniform magnetic field is described by R = mv/qB, so the radius of the particle's path is proportional to its mass. Thus if mass is doubled, radius is also doubled. 

A magnetic force can accelerate a charged particle by changing the direction of its velocity, but cannot change the magnitude of velocity.

If the magnetic field has any components perpendicular to the particle's initial velocity, the particle will experience a force according to the equation:

This force is generated perpendicular to the particle's path and will cause a change in the direction of the particle's velocity. If the magnetic field is parallel to the initial velocity, the particle will experience no magnetic force, and its path will remain unchanged. It is not possible for the particle to accelerate in the magnetic field without changing direction.

The equation for finding the force on a charge in a magnetic field is

F = qvBsinθ

Where q is charge in coulombs, v is the velocity of the charge, and B is the strength of the magnetic field in Teslas. Since the charge is moving perpendicular to the magnetic field, sinθ =1. Therefore we solve for force by plugging in the values and multiplying.

The force of a charge in a magnetic field is given by the equation . q is the charge, v is the velocity, and B is the magnetic field strength.

Additionally, the force on a current-carrying carrying wire in a magnetic field is given by the equation . I is the current, L is the length or the wire, and B is the magnetic field strength.

Because we assume the angle to be 90^o , we can set the two force equations equal to each other, and derive the equation .

By manipulating the variables, we can generate the equation . None of the other answer choices can be derived from these equations.

To determine the direction the charge will accelerate, use the right hand rule for magnetic force. To begin, hold out your hand and give a "thumb up," now rotate your wrist  clockwise so that your thumb is in the direction of the velocity of the charge. Next, extend your index finger so you are pointing into the plane of the page/screen with it, with your palm facing up. Now rotate your wrist so your index finger points in the direction of the magnetic field lines. Now your index finger should be pointing down, with your palm facing the screen/page, and your thumb still pointing to the right. The direction of the magnetic force felt by a positive charge is perpendicularly from your palm outwards, into the plane of the page/screen. Note that if the charge were negative, the direction of the magnetic force felt by the charge would be coming perpendicularly from the top of your hand instead.