An electron and a proton execute uniform circular motion in the presence of a uniform magnetic field.

If the radius of the circle is the same for both particles, which of the following statements is true?

A)Both particles move in the same direction; the electron moves faster than the proton.
B)Both particles move in the same direction; the proton moves faster than the electron.
C)The electron and the proton move in opposite directions but they move with the same speed.
D)The electron and the proton move in opposite directions; the electron moves faster than the proton.
E)The electron and the proton move in opposite directions; the proton moves faster than the electron.

The electron and proton have opposite charges and very unequal masses. The opposite charges meas that the proton bends to the right while moving through a B field that is pointed up, while an electron bends the opposite way. Thus the move in circles in opposite directions.

That leaves you with choices C, D and E.

The relationshp between charge, velcoity and mass is:

m V^2/R = q V B
R = m V/(q B)
Since the R's and B are the same, as well as q (except for sign), V is inversely proportional to m. The electrons travel 1836 times faster.

BqV=mv^2/r

Bqr/v = m

so if m is greater, v must be smaller. Obviously, they are in opposite directions.

To answer this question, we need to consider the relationship between the speed of a charged particle moving in a circular path and the radius of that path in the presence of a uniform magnetic field.

The speed of a charged particle in circular motion can be determined by the following equation:

F = qvB

Where:
- F is the magnetic force acting on the charged particle
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field strength

The magnetic force acting on a charged particle moving in a circular path is given by:

F = mv²/r

Where:
- m is the mass of the particle
- v is the velocity of the particle
- r is the radius of the circular path

Equating these two expressions for the force, we have:

qvB = mv²/r

Simplifying the equation, we find:

v = qBr/m

From this equation, we can conclude that the speed of the particle is directly proportional to the magnetic field strength, the charge of the particle, and the radius of the circular path, and inversely proportional to the mass of the particle.

Now, let's analyze the given options:

A) Both particles move in the same direction; the electron moves faster than the proton.
This statement contradicts our previous findings since the equation states that the speed is directly proportional to the charge. Therefore, the electron, having a smaller mass and the same charge as the proton, would move faster.

B) Both particles move in the same direction; the proton moves faster than the electron.
This statement also contradicts our previous findings for the same reasons as option A. The proton, having a larger mass and the same charge as the electron, would move slower, not faster.

C) The electron and the proton move in opposite directions but they move with the same speed.
According to our equation, the speeds of the particles are proportional to their charges. Therefore, the electron, having a smaller mass and the same charge as the proton, would have a higher speed. This statement is incorrect.

D) The electron and the proton move in opposite directions; the electron moves faster than the proton.
This statement aligns with our previous findings. The electron, having a smaller mass and the same charge as the proton, would move faster. Additionally, the particles would move in opposite directions due to their opposite charges.

E) The electron and the proton move in opposite directions; the proton moves faster than the electron.
This statement contradicts our previous findings since the equation states that the speed is directly proportional to the charge. Therefore, the electron, having a smaller mass and the same charge as the proton, would move faster.

Based on the analysis, the correct statement is:

D) The electron and the proton move in opposite directions; the electron moves faster than the proton.