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## Homework Statement

Hello. I'm stuck on some question, will glad if you can give me a little hint.

The problem is this:

A charge -q is located at the distance 's' above a plane, which charged in a positive charge density for area unit σ > 0 .

There is a sphere with the radius R charged on a density for volume p > 0, located 3R under the plane.

the charge -q is "falling" towards the plane, touches it (It tells to ignore the friction) and keep "falling" towards the sphere.

In which time does it touches the plane, and when it reaches the center of the sphere?

## Homework Equations

## The Attempt at a Solution

Well at first I thought this question is very easy.

To know at how much time the charged "hitted" the plane I can use kinematics or the conservation of energy.

By kinematics method I can find the acceleration using the Electric Field of the plane

**( E = σ/(2*eps))**

eps * is the electric constant.

and the Electric field of the sphere that is:

0 when r < R

**when r > R
**

* I've a mistake - it's without R - only 4pi*r^2

but then i've noticed that the force that given by F = qE is not constant and therfore the acceleration is not constant.

How can I know when it will hit if the acceleration is a function of the distance to the sphere?

thank you.

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