- #1
fatpotato
- Homework Statement
- Find the speed of a particle initially at rest when put next to a charged sphere.
- Relevant Equations
- Potential energy
Kinetic energy
Hello,
I have a particle at point A with charge , and an unmovable sphere of radius at point B with a volumic charge density . The distance from particle A to the centre of the sphere in B is . Both objects have opposed charges, so, the particle in A, initially at rest, is attracted to the charged sphere and reaches it with a certain speed with modulus , which I have to find.
First, I suppose the charge of the sphere is simply .
Then, I suppose that the electric potential energy will be entirely converted into kinetic energy , when the particle reaches the sphere. I assume (and it might be wrong) that the sphere can be considered as a particle, so I consider that the two objects will touch after the particle travels a distance although in reality it touches the sphere after traveling a distance .
In the end, it boils down to So I solve for : while removing my negative sign due to the product to avoid a complex result.
However, my answer differs from the correction. Speed should be , but I get using the following numerical values :
, , , , ,
Can anyone pinpoint what I am doing wrong please?
Thank you
I have a particle at point A with charge
First, I suppose the charge of the sphere is simply
Then, I suppose that the electric potential energy will be entirely converted into kinetic energy
In the end, it boils down to
However, my answer differs from the correction. Speed should be
Can anyone pinpoint what I am doing wrong please?
Thank you