Question
Why is the electric field inside a hollow conductor zero, and how does this principle enable electrostatic shielding (Faraday cage)?
Solution — Step by Step
In electrostatic equilibrium, free charges in a conductor rearrange until the internal electric field becomes zero. All excess charge resides on the outer surface. This is a direct consequence of the fact that if any field existed inside, the free electrons would keep moving — contradicting equilibrium.
Draw a Gaussian surface just inside the conductor wall, enclosing the hollow cavity. Since everywhere on this surface (it is inside conducting material):
No net charge exists on the inner surface (assuming no charge placed inside the cavity). The cavity is charge-free and field-free.
Even if we place the conductor in an external electric field, the free charges on the conductor redistribute to cancel the external field inside. The outer surface develops induced charges, but the inner cavity remains at .
This is electrostatic shielding — the hollow region is completely protected from external electric fields.
graph TD
A[External Electric Field Applied] --> B[Conductor Surface]
B --> C[Free charges redistribute on outer surface]
C --> D[Induced charges cancel external field inside]
D --> E[Hollow interior: E = 0]
E --> F[Objects inside are shielded]
G[Faraday Cage Applications] --> H[Lightning protection in cars/aircraft]
G --> I[MRI room shielding]
G --> J[Electronic device EMI shielding]
G --> K[Microwave oven screen]A Faraday cage is just a practical hollow conductor — it can even be a mesh (as long as mesh gaps are much smaller than the wavelength of the field being shielded).
Why This Works
The core physics is simple: conductors have free charges that respond to any internal field by moving until that field vanishes. A hollow conductor extends this principle — the cavity becomes a field-free zone regardless of what happens outside.
This is why you are safe inside a car during a lightning strike. The metal body acts as a Faraday cage, guiding the charge along the outer surface to ground.
For CBSE boards, remember two key statements: (1) electric field inside a conductor is zero in equilibrium, and (2) the cavity of a conductor is shielded from external fields. These earn full marks in the 3-mark derivation question.
Alternative Method
We can also reason using the concept of equipotential surfaces. Since the entire conductor is at a single potential in equilibrium, and , a region of constant potential has zero gradient — hence zero field. The cavity, being bounded by the conductor (all at one potential), must also be at that same potential everywhere, giving .
Common Mistake
Students often think that placing a charge INSIDE the cavity changes nothing. Wrong — if you place a charge inside the cavity, a charge appears on the inner surface and on the outer surface. The shielding works only one way: external fields cannot enter, but internal charges DO affect the outside. This distinction is a favourite JEE question trap.