Answer :
If an electric dipole is placed inside a hollow sphere, the electric field of the dipole is not zero inside the sphere. Here’s why:
Understanding the Dipole and Its Field
An electric dipole consists of two equal and opposite charges separated by a small distance. The electric field due to a dipole has a specific spatial configuration characterized by the following properties:
- The field lines emerge from the positive charge and terminate at the negative charge.
- The electric field decreases with distance from the dipole and exhibits a unique angular dependence.
Electric Field Inside the Hollow Sphere
When an electric dipole is placed inside a hollow sphere, the field due to the dipole exists within the sphere. The hollow sphere, assuming it is made of a non-conducting material, does not influence the electric field of the dipole. Therefore, the electric field inside the sphere is solely determined by the configuration of the dipole itself.
Boundary Conditions and Gauss’s Law
The scenario changes if the hollow sphere is a conducting material:
- Inside a conducting hollow sphere, the electric field must be zero in electrostatic equilibrium. This is because any free charge on the conductor would move to the surface to counteract any internal electric field, ensuring that the net electric field inside the conductor is zero.
- However, since we are dealing with the region inside the hollow (which is not within the material of the conductor), the electric field from the dipole can still exist in the hollow region.
Justification Using Gauss’s Law
Applying Gauss’s Law can provide additional insights:
- Gauss’s Law states that the electric flux through a closed surface is proportional to the enclosed charge. For a dipole, the total charge enclosed by any Gaussian surface is zero because the charges are equal and opposite.
- Despite the net charge being zero, the dipole creates a non-uniform electric field, which is not zero. The field lines have a specific pattern that results from the superposition of the fields due to each charge of the dipole.