How Does Smearing Charge dQ Uniformly on a Sphere Maintain Constant Energy?

In summary, a sphere of radius r with a uniformly distributed charge Q throughout its volume has a potential energy of Q dQ/4\pi\epsilon_{0} when a charge dQ is brought in from infinity and deposited uniformly over the surface. This can be derived by considering the electric field due to Q as a point charge and noting that distributing dQ tangentially on the sphere does not change the energy. This concept is important for understanding potential energy in electrostatics, particularly for first year physics undergraduates.
  • #1
hasan_researc
170
0
A sphere of radius r contains a charge Q distributed uniformly throughout its volume. Charge dQ is brought in from infinity and deposited uniformly over the surface. The potential energy of the charge dQ is [tex]Q dQ/4\pi\epsilon0[/tex].

This follows naturally from the result for the potential of 2 point charges after noting
(a) E due to Q is the same as a point charge and
(b) smearing dQ around the sphere (i.e., tangential to the radial direction) doesn’t change the energy.

Why/how does "smearing dQ around the sphere (i.e., tangential to the radial direction) not change the energy"?

Thanks in advance for any help!

[N B : I am a first year physics undergraduate.]
 
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  • #2
I am sorry for the poor latex code. The potential energy expression should read [tex]Q dQ/4\pi\epsilon_{0}[/tex]
 
  • #3
Mistaken for the second time now. The potential energy expression should read [tex]Q dQ/4\pi\epsilon_{0}r[/tex]
 

Related to How Does Smearing Charge dQ Uniformly on a Sphere Maintain Constant Energy?

1. What is electric potential energy?

Electric potential energy is the energy that an object possesses due to its position in an electric field. It is a type of potential energy that is associated with the interaction between electrically charged particles.

2. How is electric potential energy calculated?

The electric potential energy between two charged objects can be calculated using the equation U = k * (q1 * q2)/r, where U is the electric potential energy, k is a constant, q1 and q2 are the charges of the objects, and r is the distance between them.

3. What factors affect electric potential energy?

The electric potential energy of a system is affected by the magnitude of the charges, the distance between the charges, and the medium in which they are located. The electric potential energy also depends on the direction and orientation of the charges.

4. What is the difference between electric potential energy and electric potential?

Electric potential energy is a measure of the energy stored in a system of charges, while electric potential is a measure of the potential energy per unit charge at a specific point in an electric field. In other words, electric potential is the electric potential energy per unit charge.

5. Can electric potential energy be converted into other forms of energy?

Yes, electric potential energy can be converted into other forms of energy, such as kinetic energy or thermal energy. For example, when a charged object is released from a high potential energy point, it will convert into kinetic energy as it moves towards a lower potential energy point.

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