Classical mechanics electrostatics and charges

[timetraveller123]

Homework Statement

hi i was doing a practice physics junior olympiad paper when i got stuck in question 11 in this link
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https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf

Edit by moderator: Inserted relevant extract of the PDF so that helpers do not have to go off-site, download a PDF, and search through it for the problem statement. By the way, it was problem 10, not problem 11

what exactly does the question mean by grazing past the sphere does it mean the proton stops moving or does it continue moving and is the approach for the problem conservation of energy or some other approach.
i know a calculus based approach will work but this competition does not require the use of calculus so please don't give me a calculus approach. and how exactly does the variable l affect the trajectory of the particle i am confused please help? any help will be appreciated thanks!

Homework Equations

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

The Attempt at a Solution

 

[willem2]

what exactly does the question mean by grazing past the sphere does it mean the proton stops moving or does it continue moving and is the approach for the problem conservation of energy or some other approach.
i know a calculus based approach will work but this competition does not require the use of calculus so please don't give me a calculus approach. and how exactly does the variable l affect the trajectory of the particle i am confused please help? any help will be appreciated thanks!

If the proton or electron grazes the sphere, there will only be tangential speed. (in the direction perpendicular to the line from O to wherever the ). You should be able to use conservation of energy to find out what that speed is. After that there's another conservation law you can use to find l.

 

[timetraveller123]

If the proton or electron grazes the sphere, there will only be tangential speed. (in the direction perpendicular to the line from O to wherever the ). You should be able to use conservation of energy to find out what that speed is. After that there's another conservation law you can use to find l.

wait i don't understand how you can find out l with conservation law please i don't see it sorry!

 

[willem2]

Can you use conservation of energy to compute the speed of the proton when it's grazing the disk?

 

[timetraveller123]

Can you use conservation of energy to compute the speed of the proton when it's grazing the disk?

yay that i think i should be able to do given the initial energy and the final distance for the sphere is r so the final speed i know how to calculate but how does that help you to calculate l