You can check out this one first!.... https://brilliant.org/problems/focused-electric-field/?ref_id=1480760
Now my question is something different, Say we have a rectangular hyperbola, of which the right hand part is charged with linear charge density and the left one with .
There is a Rod Lying on the y-axis, with mass , Lenght and its center is kept at . It is charged with, say surface charge density, .
Check out the image.
This is it.
So We need to find the acceleration of the rod, as soon as we release it.
SOLUTION AS DONE BY ME (Not sure if correct).
If we draw the interaction between one element from the hyperbola to the rod, we can see that, The net force acting is in the X-direction and the Y- direction cuts off.
And The force from two opposite charged hyperbola on the rod will add up and will be like .
Here (x,y) is the position of the charges on the hyperbola. and is the distance from the center of the rod to the element. and is the acute angle made by the rod with the line joining the element of rod and hyperbola.
We know whereas dq = ,
now putting these in the equation the force of interaction on the Rod comes out to be,
I want you guys to verify if I am correct at every places and our expression comes same.
Thanks For Helping and Reading!
Question is original.
Please do the verification fast! I want to make a question on this and post it! And if you can do the integral, please tell me what comes.