# Minimum speed of the bullet to penetrate a sphere

**1. The problem statement, all variables and given/known data**

A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

**2. Relevant equations**

**3. The attempt at a solution**

I think if the bullet can just reach the center ,then it can penetrate through the sphere because the electric field inside a sphere is radially outwards .As it reaches the center and moves just a little bit outwards radially ,the electric field will push the bullet outwards .

The problem can be approached either by conservation of energy or by work kinetic energy theorem.

1) By conservation of energy

kq^{2}/R+(1/2)mu^{2} = (3/2)kq^{2}/R

2) By work energy theorem

## \int_{R}^{0}\frac{kq^{2}r}{R^3} \hat{r} \cdot dr\hat{r} = \frac{1}{2}mu^2 ##

Have I approached the problem correctly or is there something more in it ?

http://ift.tt/1hR9UQe

## Leave a comment