a hollow conducting shere of radius R has a charge Q placed on its surface. what is the electric field and potential inside the sphere?
To find the electric field and potential inside the hollow conducting sphere, we need to understand the concept of Gauss's law and the properties of conductors.
Gauss's law states that the total electric flux through a closed surface is proportional to the charge enclosed by the surface. In other words, the electric field inside a conductor in electrostatic equilibrium is always zero.
Since the electric field inside the hollow conducting sphere is zero, there can be no potential difference or electric potential, as the electric field is the negative gradient of electric potential. Therefore, the electric potential inside the hollow conducting sphere is constant and equal to the potential on its surface.
In this case, the charge Q is placed on the outer surface of the sphere. Due to the electrostatic equilibrium, the charge redistributes itself on the outer surface such that the electric field inside the conductor is zero.
Hence, the electric field inside the hollow conducting sphere is zero, and the electric potential is constant and equal to the potential on the surface of the sphere, which is Q/4πε₀R, where ε₀ is the permittivity of free space.
In summary:
- The electric field inside a hollow conducting sphere is zero.
- The electric potential inside a hollow conducting sphere is constant and equal to the potential on its surface, which can be calculated using the formula Q/4πε₀R.