Finding charge on sphere using energy

1. Apr 4, 2014

need_aca_help

1. The problem statement, all variables and given/known data
a) What charge would need to be placed on a metal sphere such that the electric field produced stored a total of 50 J if the radius of the sphere was 18 cm?
b) How much work would need to be done to reduce the radius to 9 cm, assuming the sphere is (mechanically) easily compressible?

2. Relevant equations
V=(4/3)pi r2

3. The attempt at a solution
Not sure where to tackle this problem...

2. Apr 5, 2014

Simon Bridge

How much work to get the first smallest bit of charge onto the sphere (from infinity)?
The bit after that?
... spot the pattern.

Either that or look up the equation for the amount of energy stored in a charged metal sphere.

3. Apr 5, 2014

need_aca_help

I found this equation from the text book.

u = 2keQ2 / R

Using this I get

50 = 2(9X109)Q2 / 0.18
0.18(50) = 2keQ2
Q2 = 9 / 2k
Q = square root (9 / 2(9X109)
Q = 2.23607 X 10-5
2.24X10-5 C

But this isn't right...

4. Apr 5, 2014

Simon Bridge

So how can you tell if it is the right equation?

i.e. read the book carefully: what exactly does it say this is the energy of?

5. Apr 5, 2014

need_aca_help

Energy stored by a charged sphere

6. Apr 5, 2014

Simon Bridge

... is that exactly what it says?

Not just what's written down - there is usually a diagram as well.

i.e. is the sphere uniformly charged? Is the charge distributed through the whole volume or just on the surface? Is the sphere a conductor or an insulator?

If you cannot narrow this down you will have to do some calculus.

7. Apr 6, 2014

need_aca_help

I managed to solve the problem, using this equation:
E = 1/2QV
E = 1/2Q(kQ/r)

8. Apr 6, 2014

Simon Bridge

Well done ... more careful reading?