Voltage of a charged conducting sphere

In summary, the conversation discusses the concept of voltage remaining constant inside a charged conduction sphere, even at the surface where there is an electric field present. The potential does change slightly as you move towards the surface, but the change is infinitesimal due to the integration of the electric field. An analogy of a step function is used to further explain this concept.
  • #1
maccha
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I've recently learned that the voltage of a charged conduction sphere remains constant inside the sphere all the way to the surface, as the electric field inside is zero. What I don't understand is how the voltage can be the same on the surface as it is inside- since there is an electric field on the surface, wouldn't the potential change?
 
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  • #2
maccha said:
I've recently learned that the voltage of a charged conduction sphere remains constant inside the sphere all the way to the surface, as the electric field inside is zero. What I don't understand is how the voltage can be the same on the surface as it is inside- since there is an electric field on the surface, wouldn't the potential change?

As you increase r to the surface, the potential does change, but infinitesimally with any infinitesimal increase in r. The electric field can change dramatically, as you have pointed out. But you need to integrate E to get V.

If it helps, let me pose you this question. Consider a step function where y jumps straight up from 0 to 1 at x = 10. What's the area under the curve from x = 0 to x = 9.999999? What's the area under the curve from x = 0 to x = 10.0001?
 

1. What is the equation for calculating the voltage of a charged conducting sphere?

The voltage of a charged conducting sphere can be calculated using the equation V = kQ/r, where V is the voltage, k is the Coulomb's constant, Q is the charge on the sphere, and r is the radius of the sphere.

2. Can the voltage of a charged conducting sphere be positive or negative?

Yes, the voltage of a charged conducting sphere can be either positive or negative. A positive voltage indicates that the sphere is positively charged, while a negative voltage indicates a negative charge.

3. How does the voltage of a charged conducting sphere change with distance?

The voltage of a charged conducting sphere follows an inverse relationship with distance. As the distance from the sphere increases, the voltage decreases. This can be seen in the equation V = kQ/r, where r is in the denominator.

4. Can the voltage of a charged conducting sphere be affected by external electric fields?

Yes, the voltage of a charged conducting sphere can be affected by external electric fields. If an external electric field is applied, the voltage of the sphere will change, as the charges on the surface will redistribute to reach a new equilibrium.

5. How does the voltage of a charged conducting sphere differ from that of a point charge?

The voltage of a charged conducting sphere is different from that of a point charge in that the voltage of a sphere is constant at all points on its surface, while the voltage of a point charge decreases with distance. The voltage of a sphere is also affected by the size and charge of the sphere, while a point charge has a fixed voltage value.

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