Force on Charge Moving in Magnetic Field

In summary, the question discusses the circular motion of a proton, deuteron, and alpha particle in a uniform magnetic field, all accelerated by the same potential difference. The radius of their paths can be determined using the formula r = mv/qB, and by finding the velocity of each particle and comparing them. The charge of a proton is confirmed to be 1.6E-19 C, but is not necessary for solving the problem.
  • #1
Kandycat
22
0

Homework Statement


A proton (mass mp), a deutron (m=2mp, Q = e), and an alpha particle (m = 4mp, Q = 2e) are accelerated by the same potential difference V and then enter a uniform magnetic field B, where they move in circular paths perpendicular to B. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton.

Homework Equations


r = mv/qB

r= radius
m=mass
v=velocity
q=charge
B=magnetic field

The Attempt at a Solution


I thought V = delta PE = delta KE = delta (1/2)mv2

And then I got confused.
 
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  • #2
When the charged particles are accelerated in a potential difference V,energy acquired by them is given by qV, where q is the charge on it. And it can be equated to its KE. First of all find the velocity of each particle and substitute in the formula for radius and compare them.
 
  • #3
Is the charge of a proton 1.6E-19 C?
 
  • #4
Yes. But to solve this problem this value in not needed, because you are comparing radii.
 

1. What is the force on a charge moving in a magnetic field?

The force on a charge moving in a magnetic field is known as the Lorentz force, and it is given by the equation F = qvBsinθ, where q is the charge of the particle, v is its velocity, B is the strength of the magnetic field, and θ is the angle between the velocity and the magnetic field.

2. How does the direction of the magnetic field affect the force on a moving charge?

The direction of the magnetic field affects the direction of the force on a moving charge, as the force is always perpendicular to both the velocity of the charge and the magnetic field. If the velocity and magnetic field are parallel, the force will be zero, and if they are antiparallel, the force will be in the opposite direction.

3. What is the relationship between the magnitude of the charge and the force on a moving charge in a magnetic field?

The force on a moving charge in a magnetic field is directly proportional to the magnitude of the charge. This means that the greater the charge of the particle, the stronger the force it will experience in a given magnetic field.

4. How does the velocity of the charge affect the force in a magnetic field?

The velocity of the charge affects the force in a magnetic field in two ways. First, the magnitude of the force is directly proportional to the velocity, meaning that a faster-moving charge will experience a stronger force. Second, the direction of the force is perpendicular to the velocity, so the angle between the velocity and the magnetic field will also affect the magnitude of the force.

5. Are there any other factors that can affect the force on a moving charge in a magnetic field?

Yes, there are a few other factors that can affect the force on a moving charge in a magnetic field. These include the strength and direction of the magnetic field, the charge's mass, and any external forces acting on the charge. Additionally, the type of particle (e.g. electron vs proton) can also affect the force due to differences in charge and mass.

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