Proton trajectory grazing a charged sphere

In summary, the angular momentum of the proton, which is conserved, is constant during its motion around the nucleus.
  • #1
timetraveller123
621
45

Homework Statement


upload_2017-2-11_10-28-38-png.112937.png


Homework Equations


potential energy = -kQq/r
potenial = kQ/r

The Attempt at a Solution


i am not quite sure how does l play a part in this experiment since it is far away l is insignificant and the only initial energy is kinetic energy and final is kinetic and electric potential energy i can calculate the final electric potential energy and initial kinetic energy is given so hence at most i can only calculate final kinetic energy but how is that going to help me find l[/B]
 
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  • #2
vishnu 73 said:

Homework Statement


upload_2017-2-11_10-28-38-png.112937.png

The Attempt at a Solution


i am not quite sure how does l play a part in this experiment since it is far away l is insignificant and the only initial energy is kinetic energy and final is kinetic and electric potential energy i can calculate the final electric potential energy and initial kinetic energy is given so hence at most i can only calculate final kinetic energy but how is that going to help me find l[/B]
It is a central force field, there is one more conserved quantity, what is it?
 
  • #3
Moderator note: Thread title changed to better describe the problem. Previous title was too general (forum rules on thread titles).
 
  • #4
is it the work done on the proton?
 
  • #5
vishnu 73 said:
is it the work done on the proton?
Why should it be constant during the motion of the proton?
 
  • #6
vishnu 73 said:

Homework Statement



Homework Equations


potential energy = -kQq/r
potenial = kQ/r

The Attempt at a Solution


i am not quite sure how does l play a part in this experiment since it is far away l is insignificant and the only initial energy is kinetic energy and final is kinetic and electric potential energy i can calculate the final electric potential energy and initial kinetic energy is given so hence at most i can only calculate final kinetic energy but how is that going to help me find l[/B]

In a central force field, like that, the angular momentum also conserves.
 
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  • #7
oh wow that is really smart is it because the force is constantly radially out ward hence no net torque on proton about the centre of sphere
so ,
initial energy = final energy
2000eV = 1000ev + 1/2 m vf2
vf = √(2000ev/m)

then by what you said conservation of angular momentum i am assuming you meant about the centre of sphere

hence
m ri x vi = m rf x vf
ri x vi = rf x vf
letting distance o to o' be s
√(l2 + s2) √(4000ev/m) sinθ = R √(2000ev/m)
√(l2 + s2) l/(√(l2 + s2)) = R /√2
l = R/√2
am i right for part a by the way thanks for the amazing insight really inspiring question
 
  • #8
vishnu 73 said:
l = R/√2
am i right for part a by the way thanks for the amazing insight really inspiring question
It is right, good work!
 
  • Like
Likes timetraveller123
  • #9
omg thanks so much that one hint of yours helped me so much i was initially initially thinking of calculus
 

1. What is a proton trajectory grazing a charged sphere?

A proton trajectory grazing a charged sphere refers to the path that a proton takes as it approaches and passes by a charged sphere. This phenomenon is often studied in the field of particle physics and can provide insights into the interactions between charged particles and electric fields.

2. How does the charge of the sphere affect the proton trajectory?

The charge of the sphere plays a crucial role in determining the trajectory of the proton. A positively charged sphere will attract the negatively charged proton, causing it to curve towards the sphere. On the other hand, a negatively charged sphere will repel the proton, causing it to curve away from the sphere. The strength of the electric field around the sphere will also affect the trajectory of the proton.

3. What factors besides charge influence the proton trajectory?

The mass and velocity of the proton are also important factors that can influence its trajectory. A proton with a higher velocity will have a different trajectory than a slower-moving proton. Additionally, the distance between the proton and the sphere, as well as the size of the sphere, can also impact the trajectory of the proton.

4. Are there any real-life applications of studying proton trajectory grazing a charged sphere?

Yes, there are several real-life applications of studying this phenomenon. One example is in medical imaging, where charged particles are used to create images of the human body. Understanding how these particles interact with charged spheres can help improve the accuracy of these imaging techniques. It is also relevant in the development of particle accelerators and other technologies that involve the manipulation of charged particles.

5. Are there any mathematical equations or models that describe proton trajectory grazing a charged sphere?

Yes, there are several mathematical equations and models that can be used to describe this phenomenon. One example is the Coulomb's Law, which calculates the electric force between two charged particles. Other models, such as the Lorentz force law and the equations of motion, can also be used to describe the trajectory of a proton in an electric field. These equations are often used in simulations and experiments to study proton trajectory grazing a charged sphere.

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