Calculation of potential of an grounded sphere ball with charges

In summary, the conversation discusses a neutral conductor sphere with a cavity and a point charge inside. The conductor is grounded and the question asks for the electric potential outside the conductor and the total charge on the conductor. The figure drawn suggests that the E-field and potential are zero by Gauss law, but the conversation notes that this may not be possible given the follow-up questions related to the potential. The speaker is seeking assistance in identifying any mistakes in the figure.
  • #1
henry407
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Homework Statement


Consider an originally neutral conductor sphere of radius R with a cavity and a point charge Q1 inside the cavity.
(a)The conductor is grounded. Find the electric potential outside the conductor and the total charge on the conductor.

Homework Equations



The Attempt at a Solution


As shown on the figure I draw, I conclude that the E-field and the potential is zero by gauss law. Somehow, I think that is not possible as this question is followed up by 3 other questions which related to its potential. I hope someone could point out the mistake of the figure. Thanks a lot~
 

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Help~
 

FAQ: Calculation of potential of an grounded sphere ball with charges

How do you calculate the potential of a grounded sphere ball with charges?

The potential of a grounded sphere ball with charges can be calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb's constant (9x10^9 Nm^2/C^2), Q is the total charge on the sphere, and r is the distance from the center of the sphere to the point where the potential is being calculated.

What is the significance of grounding in this calculation?

Grounding in this calculation refers to connecting the sphere to an infinite reservoir of charges, such as the Earth. This allows for the redistribution of charges on the sphere and ensures that the potential at the surface of the sphere is zero.

How does the potential change as the distance from the sphere increases?

The potential decreases as the distance from the sphere increases. This can be seen in the inverse relationship between potential and distance in the formula V = kQ/r.

Can the potential of a grounded sphere ball with charges ever be negative?

Yes, the potential can be negative if the total charge on the sphere is negative. This indicates that the electric field is directed towards the sphere, rather than away from it.

What is the difference between potential and electric field?

Potential is a scalar quantity that describes the amount of work needed to move a unit positive charge from one point to another in an electric field. Electric field, on the other hand, is a vector quantity that describes the force per unit charge acting on a test charge at a given point in space.

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