Proton trajectory grazing a charged sphere

[timetraveller123]

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]

 

[ehild]

Homework Statement

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?

 

[gneill]

Moderator note: Thread title changed to better describe the problem. Previous title was too general (forum rules on thread titles).

 

[timetraveller123]

is it the work done on the proton?

 

[ehild]

is it the work done on the proton?

Why should it be constant during the motion of the proton?

 

[ehild]

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.

 

[timetraveller123]

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 v_f²
v_f = √(2000ev/m)

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

hence
m r_i x v_i = m r_f x v_f
r_i x v_i = r_f x v_f
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

 

[ehild]

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!

 

[timetraveller123]

omg thanks so much that one hint of yours helped me so much i was initially initially thinking of calculus