8.1 Properties of conductor

  Electrostatics

1. The electrostatic field is zero inside a conductor: When an electrostatic field exists, the free electrons in a conductor move in opposite direction and an opposing field inside the conductor is created. As a result of redistribution of charges, there is no net electric field inside the conductor.
   
   
   
   
   
2. The electric field on the surface of a conductor is normal to the surface: The component of electric field parallel to the surface will cause free electrons to move, it is clear that the electric field is normal to the surface.
   
   
3. The electrostatic field inside a cavity of a conductor is zero
   
   Case I: In presence of an external electrostatic field, the net electric field inside a cavity of a conductor will be always zero.
   
   Reason: Property 1
   
   This phenomenon gives rise to very important concept known as electrostatic shielding.
   
   Electrostatic shielding: It is the process of isolating a certain region of space from external field. It is based on the fact that electric field inside a conductor is zero. Electrostatic shielding is the best way to protect the sensitive electronic instrument from the influence of an external electric field.
   
   
   
   
   
   Case II: When a charge $+q$ is placed at the center of a cavity of an electrically neutral spherical conductor, then also the net electric field inside a cavity is zero.
   
   Reason: The charge $+q$ placed at the center of a cavity induces charge $-q$ at the outer surface of the cavity as shown in figure (b). Now, the conductor becomes electrically neutral. So, we have no excess charge within the metal.
   
   Now since an induced charge $-q$ appears on the surface of the cavity, a charge $+q$ must be induced on the outer surface of the conductor as shown in figure (c). So, the positive charge on the outer surface generates electric field lines that radiate outward as if they originated from the central charge and the conductor were absent. The conductor does not shield the outside from the field produced by the charge on the inside.
   
   
   
   
   
   
4. The electrostatic potential is constant inside a conductor: As there is no electric field inside the conductor, the electrostatic potential inside a conductor is constant.
   
   
5. Interior of a conductor has no excess charge in the static situation: Excess charges resides on the surface of the conductor.
   
   Note: As there is no electrostatic field inside a conductor, it can be seen with the help of Gauss theorem that no net charge can exist inside a conductor.
   
   
6. Electric field at the surface of a charged conductor is $\frac{\sigma }{{{\varepsilon _0}}}\widehat n$.
   
   
7. For a nonuniform conductor the surface charge density $\left( \sigma \right)$ varies inversely proportional to the radius of curvature $(r)$ for that part of the conductor, i.e.,
   $$\sigma \propto \frac{1}{{{\text{radius of curvature }}\left( r \right)}}$$
   
   
   
   As, $${r_B} > {r_A}$$ So, $${\sigma _A} > {\sigma _B}$$ Also, $${E_A} > {E_B}$$