What is the total energy of the point charge?

In summary, the conversation discusses the motion of a point charge, with a mass and charge opposite that of a uniformly distributed solid sphere, as it is released on the surface of the sphere. The motion is described as simple harmonic with a time period of T and the total energy of the point charge is given by E. The electric field inside the sphere is found using Gauss' Law and the force acting on the charge is calculated using Newton's Laws. The energy of the point charge is also calculated using a specific expression.
  • #1
meadow
19
0
I need help with this question. I can't see the motion. I have

Consider a solid sphere of radius R with a charge Q distributed uniformly. Suppose that a point charge 'q' of mass 'm', with a sign opposite that of Q, is free to move within the solid sphere. Charge q is placed at rest on the surface of the solid sphere and released. Describe the subsequent motion. In particular, what is the period of the motion, and what is the total energy of the point charge?

HELP!
 
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  • #2
If the charge is free to move through the sphere,the motion will be a simple harmonic one
with time period=T where T is given by
[tex]T=2 \pi \sqrt{\frac{4 \pi \epsilon_0 R^3 m}{Qq}}[/tex]
 
  • #3
Assume the charge will not disturb the charge density of the sphere. Use Gauss' Law to find the electric field inside the sphere. I think it's obvious what your Gaussian surface should be.
After you've found the electric field as a function of position (or distance from the sphere), you can simply calculate the force acting on the charge and use Newton's Laws to find its motion.
 
  • #4
Energy of point charge is given by E where E is given by the expression that is written below
[tex]E=-\frac{Qq}{4 \pi \epsilon_0 R}[/tex]
 

1. What is the definition of total energy of a point charge?

The total energy of a point charge is the sum of its kinetic energy, potential energy, and rest energy. It is a measure of the amount of energy associated with the charge's motion and position in a given system.

2. How is the total energy of a point charge calculated?

The total energy of a point charge is calculated using the equation E = K + U + mc^2, where E is the total energy, K is the kinetic energy, U is the potential energy, and m is the mass of the charge. The speed of light, c, is also included in the equation.

3. What is the unit of measurement for total energy of a point charge?

The unit of measurement for total energy of a point charge is joules (J). This is the standard unit for measuring energy in the SI system.

4. Can the total energy of a point charge be negative?

Yes, the total energy of a point charge can be negative. This indicates that the charge has more potential energy than kinetic energy, and it is usually associated with a bound system where the charge is confined by an electric potential.

5. How does the distance between two point charges affect the total energy?

The distance between two point charges affects the total energy through the potential energy term in the equation. As the distance increases, the potential energy decreases, resulting in a decrease in the total energy. This demonstrates the inverse relationship between potential energy and distance in an electric field.

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