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. 

This question requires knowlegde of the right-hand rule. Point the fingers of your right hand in the direction of the electron's velocity (to the right). Point your thumb in the direction of the magnetic field (into the page). Your palm should be facing in the direction of the force on a positive particle. However, electrons are negative, so this direction must be reversed, meaning that the direction of the force is upward along the plane of the page.

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.

A photon will travel fastest through a vacuum. Photons are generally massless and can be thought of as a light wave, which travels fastest in a vacuum and slowest through a metal or solid. This can be visualized using the concept of the index of refraction, which describes the speed of light through air compared to the speed through other mediums. A vacuum will be the least dense and cause the least hindrance to a photon as it travels, thus giving it the lowest index of refraction and allowing the fastest speed of light.

The energy of a wave increases with increasing frequency and decreasing wavelength. Considering these different waves, radiowaves possess the longest wavelengths and gamma rays the shortest wavelength, thus gamma rays carry the greatest amount of energy.

In order to solve this problem, we must understand that the resistance of parallel resistors is added inversely and that series resistors are added directly.

Series

Parallel

Ohm’s Law

We can first find the total resistance of the circuit to be 4 Ω using ohm's law . Then by subtracting the resistor in series (2 Ω) from the total resistance, we can set the remaining parallel resistors equal to 2 Ω. Finally, we can use the parallel resistor equation to find R. Remember that you can simply count the two resistors in series on the far right branch of the circuit (R and 2 Ω) as one number in the parallel resistor formula giving us

we can solve for this to find that R = 2 Ω

Remember that convention dictates that current flows in the direction of positive charge (protons), thus, electrons flow in the opposite direction. Also remember that the larger length on the battery symbol on the circuit diagram indicates that current flows in this direction. In the diagram below, we can see that current flows clockwise, thus electrons flow counterclockwise.

Remember that convention dictates that current flows in the direction of positive charge (protons). Also remember that the larger length on the battery symbol on the circuit diagram indicates that current flows in this direction. In the diagram below, we can see that current flows counterclockwise.

As with resistors, capacitors in series share the same current. This is a re-statement of the law of conservation of charge. In contrast, capacitors and resistors in parallel share the same voltage.

Electric power is expressed in a number of ways. We will need to use the relationship that involves current and resistance:

We are given the current and resistance, allowing us to calculate the power.