Question

A hollow metal sphere has a potential of $\mathbf{+}\mathbf{400}\mathbf{\text{V}}$with respect to ground (defined to be at$\mathbf{\text{V=0}}$ ) and a charge of $\mathbf{5.0}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\text{C}}$. Find the electric potential at the centre of the sphere.

Short answer

The electric potential at the centre of the sphere is $+400\text{V}$.

Step-by-step solution

The given data:

Electric potential of hollow sphere with respect to ground$\mathrm{V}=0$,$\mathrm{V}=+400\text{V}$

Charge on the sphere, $\mathrm{q}=5.0\times {10}^{-9}\text{C}$

Understanding the concept of electric potential:

The electric potential of a system is directly proportional to the charge present in the system. Thus, for the given case of the hollow sphere, the charges are all present at the surface of the sphere as it is a conductor. Thus, the electric potential at the surface is equal to the potential at the centre of the sphere.

Calculation of the electric potential at the centre of the sphere: 

Since the electric potential throughout the entire conductor is a constant, the electric potential at its center is also$+400\text{V}$.

Hence, the value of the required potential is $+400\text{V}$.