Calculating Electric Field and Potential of a Charged Hollow Ball

AI Thread Summary
The discussion centers on calculating the electric field and potential of a charged hollow ball with uniform volume charge density. Participants emphasize using Gauss's Law to determine the electric field at specified distances from the center, noting the importance of integrating the charge distribution. For electric potential, the relationship between electric field and potential is highlighted, particularly for spherically symmetric cases. The method for finding the speed of a charge upon hitting the ball involves equating electric potential energy to kinetic energy. The original poster expresses gratitude and acknowledges a potential integration error, indicating a willingness to seek further clarification if needed.
cherrios
Messages
8
Reaction score
0
I've been having some trouble with this problem: A hollow ball that has radius=X, has uniform volume charge density of \rho.

1) Gauss's Law->Find electric field at .1X and 3X from the center

2)What is electric potential at .1X and 3X from center?

3) Find electric potential energy of charge q, with mass = m, when it is released 3X from center of the hollow ball. When it hits the ball, what is its speed?

For 3, would I have to equate electric potential energy to kinetic energy, and then solve for velocity?

Any tips would be much appreciated!
 
Physics news on Phys.org
How does the ball have a uniform volume charge density if it's hollow? I find that confusing, I think it's meant to be a solid sphere of charge.

Your method for #3 should work fine, did you do the other two okay?
 
oh sorry, it's filled with uniform volume charge
 
cherrios said:
I've been having some trouble with this problem: A hollow ball that has radius=X, has uniform volume charge density of \rho.

1) Gauss's Law->Find electric field at .1X and 3X from the center

2)What is electric potential at .1X and 3X from center?

3) Find electric potential energy of charge q, with mass = m, when it is released 3X from center of the hollow ball. When it hits the ball, what is its speed?

For 3, would I have to equate electric potential energy to kinetic energy, and then solve for velocity?

Any tips would be much appreciated!

1) Generally, when you need to find an electric field use Gauss' Law. The trick here is in the answer to the question, how much charge is inside your Gaussian surface? In this case, the charge distribution in uniform, so just integrate over the volume of the surface: q_{in} = \int_0^r \rho r^2 sin \theta dr d \theta d\phi = \rho * (4/3) \pi r^3, where r is the radius of your (hopefully spherical!) Gaussian surface. Now apply Gauss' Law. For the outside calculation remember that the object's radius ends at r = X. So we have a total charge Q = \rho * (4/3) \pi X^3.

2) Recall the relationship between the Electric Field and the Electric Potential. Now, since E is spherically symmetric, the E and V are related by a simple derivative of r.

3) Your method sounds like a plan to me. Unless you really WANT to find the force on the ball, use F = ma, then use the uniform linear acceleration equations. I'd rather use your method. :biggrin:

-Dan
 
Thank guys! I think I should be fine for now; I believe I had an integration error. I might have some questions later... but thanks again!
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top