Electric Potential of a Uniformly Charged Sphere

In summary, the conversation is discussing the electric potential of a uniformly charged sphere and the formula for it, which is \frac{1}{4\pi \epsilon_0}\frac{Qr^2}{r_0^3}. The person is having trouble deriving this formula and has tried using different methods. However, they are not able to get the correct answer and are unsure of what they are doing wrong. They also mention the difference between a sphere and a ball and question the dependence of the electric field on r. They also clarify whether the potential is being considered inside or outside of the sphere.
  • #1
Typhon4ever
51
0
My book gives the electric potential of a uniformly charged sphere as [itex]\frac{1}{4\pi \epsilon_0}[/itex][itex]\frac{Qr^2}{r_0^3}[/itex]. I can't derive this forumula. What I get is [itex]\frac{1}{8\pi \epsilon_0}[/itex][itex]\frac{Qr^2}{r_0^3}[/itex]. I can guess how the book did it which is by taking the equation for voltage of a single point charge [itex]V=\frac{1}{4\pi \epsilon_0}[/itex][itex]\frac{Q}{r}[/itex] then subbing in for Q enclosed [itex] Q\frac{r^3}{r_o^3} [/itex] which is the charge in terms of r. That would give you the book answer. I tried doing it a different way however which I'm not sure why it won't work. I used Va-Vb=[itex]\int _a^{b}[/itex] E dl. Yet when I get to solving for the electric field I get [itex]\frac{Q}{4\pi r^2 \epsilon_0}[/itex]. If I take Q out then I can solve for the book answer. However, Q is in terms of r which I wrote above so I can't take Q out. I must integrate it. That gives me the 1/8 instead of the 1/4. What am I doing wrong? Thanks!
 
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  • #2
Do you have a uniformly charged sphere, or ball? The derivation suggests a ball (charge everywhere in the volume), not a sphere. Q is the total charge, and r_0 is the radius of the ball?
How do you get the electric field? It should not depend on r like that.
 
  • #3
Are you looking for the potential inside the sphere or outside? In other words is r > r0 or is r < r0?
 

Related to Electric Potential of a Uniformly Charged Sphere

What is the formula for calculating the electric potential of a uniformly charged sphere?

The formula for calculating the electric potential of a uniformly charged sphere is V = k(Q/r), where V is the electric potential, k is the Coulomb constant (9 x 10^9 Nm^2/C^2), Q is the charge of the sphere, and r is the distance from the center of the sphere.

How does the electric potential of a uniformly charged sphere change with distance from the center?

The electric potential of a uniformly charged sphere follows an inverse relationship with distance from the center. This means that as the distance from the center increases, the electric potential decreases.

What is the difference between electric potential and electric field?

Electric potential is a measure of the potential energy per unit charge at a specific point in an electric field. It is a scalar quantity, meaning it has only magnitude. Electric field, on the other hand, is a vector quantity that describes the direction and strength of the electric force at a specific point in an electric field.

How does the electric potential of a uniformly charged sphere vary with the amount of charge on the sphere?

The electric potential of a uniformly charged sphere is directly proportional to the amount of charge on the sphere. This means that as the charge on the sphere increases, the electric potential also increases.

Is the electric potential of a uniformly charged sphere constant throughout the sphere?

No, the electric potential of a uniformly charged sphere is not constant throughout the sphere. It varies with distance from the center, and is highest at the surface of the sphere. The electric potential inside the sphere is also not uniform, and decreases as you move closer to the center.

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