The answer is not zero, so you're right about that. Think about it this way: what if instead of a sphere of continual charge, you had billions of little, positive point charges in the shape of a sphere. You could calculate the voltage of each one and sum them together to get the total voltage at that point. Well, voltage for a positive charge is always positive and never zero. Therefore, all the point charges would always add and never subtract from the voltage at some point p inside the sphere.collegeconfid said:Homework Statement
What is the electric potential at the center of a uniformly charged sphere?
Homework Equations
Ed=-VThe Attempt at a Solution
Integrate from infinity to the center of the sphere and be sure to account for the changing electric potential. I was told that the answer might be zero, but I believe that that is not right. So, am I right?
Electric potential is a measure of the energy required to move a unit of electric charge from one point to another in an electric field. It is important because it helps us understand and analyze the behavior of electric charges in various systems, such as circuits and particles.
Electric potential is a scalar quantity, meaning it has only magnitude and no direction. On the other hand, electric field is a vector quantity, meaning it has both magnitude and direction. Electric potential is related to electric field by the equation V = -∫E · dl, where V is the electric potential, E is the electric field, and dl is the displacement.
The electric potential of a sphere can be calculated using the equation V = kQ/r, where k is the Coulomb constant, Q is the charge of the sphere, and r is the distance from the center of the sphere. This equation assumes that the sphere is a point charge and that the distance from the center is much larger than the size of the sphere.
To solve for the center of a sphere using electric potential, you will need to use the equation V = kQ/r and set it equal to the potential at the center of the sphere, which is V = kQ/R, where R is the radius of the sphere. Then, solve for r to find the distance from the center to the point where the potential is being measured.
Yes, the electric potential of a sphere can be negative. This can happen if the sphere has a net negative charge, or if the potential is being measured at a point inside the sphere where the electric field is directed towards the center. In this case, the negative sign indicates that work would need to be done to move a positive test charge from infinity to that point.