how to proceed for integration type questions of electrostatics?

Question

how to proceed  for integration type  questions of electrostatics?

egenriether · Answer

Typically you need to find the equation of the differential amount of charge, dQ.  Then integrate it over the correct limits.  Without an example, that's the best I can do...

anonymous · Answer

take this exampel ,A thin semi-circular ring of radius r has a positive charge q
distributed uniformly over it. The net field E
at the centre O is

egenriether · Answer

ok, if the semi-circular ring has an even distribution of charge of charge then its linear charge density is q/L where L is the length (2*pi*r/2=pi*r).  The E field is described by each tiny amount of charge and its position relative to the observation point.  Can you recall the equation of the electric field from a point source?  You'll need that and treat each differential amount of charge dQ as a point then integrate from 0 to pi (half circle)

egenriether · Answer

This isn't the full answer.  It should be in cartesian coordinates to see that the field will be along one direction.  The field lines across the half circle will cancel and the field should point in one direction.

egenriether · Answer

https://www.youtube.com/watch?v=L1n2EUvayfw

anonymous · Answer

thanks for the help