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Properties Of Conductors In Electric Field

Properties Of Conductors In Electric Field :- When a conductor is placed in an electric field, it exhibits several distinct behaviors due to the free movement of charge within it. Below are the key properties of conductors in an electric field :

1. Free Charges (Electrons) Move Easily

Conductors contain free electrons that are not bound to any particular atom. When an external electric field is applied, these electrons experience a force and start moving opposite (and ) to the direction of the field. This movement continues until electrostatic equilibrium is reached.

2. Electric Field is Perpendicular to the Surface of a Conductor

Below figure shows the movement of a positive charge due to the effect of an external applied electric field. The motion of a positive charge is equivalent to the motion of a negative charge in the opposite direction.

The free charges move until the electric field is perpendicular to the conductor’s surface. There can not be any component of the electric field parallel to the surface of conductor in electrostatic equilibrium, since, if there were, it would produce further movement of charge.

3. Electric Field is Zero Inside a Conductor

At electrostatic equilibrium, the charges inside a conductor redistribute themselves in such a way that the net electric field within the conductor becomes zero. This occurs because the internal electric field generated by the redistributed charges exactly cancels the applied external field.

When a conductor is placed in an electric field, it is polarized. Above figure shows the result of placing a neutral conductor in an originally uniform electric field. The field becomes stronger near the conductor but entirely disappears inside it.

$\displaystyle {{\left( {{\overrightarrow{E}}_{Net}} \right)}_{Inside}}=0$

4. Conductors Shield Their Interior – Electrostatic Shielding

Conductors can act as electrostatic shields. Since the electric field inside is zero, placing sensitive equipment inside a conducting enclosure (like a Faraday cage) can protect it from external electric fields.

5. Conductors Behave as Equipotential Surfaces

Because the electric field inside is zero, there is no potential difference within the conductor. The entire conductor, including its surface, is at the same electric potential.

$\displaystyle {{\left( {{\overrightarrow{E}}_{Net}} \right)}_{Inside}}=0\Rightarrow {{V}_{inside}}=constant$

6. Charge given to a Conductors resides on its Surface

All excess charge on a conductor resides on its surface. The charges redistribute themselves in a way that minimizes repulsion between like charges, eventually leading to electrostatic equilibrium. Based on their surface characteristics, conductors can be classified into two categories :

(a) Uniform-shaped conductors – These have smooth, symmetrical surfaces where the surface charge density is uniformly distributed. For example : Sphere, smooth cylinder, flat sheet, etc.

(b) Non-uniform-shaped conductors – These have irregular surfaces, often with sharp points or edges, where charge accumulates more densely, resulting in a non-uniform surface charge distribution. For example : Pointed tip, edge, rough or irregular surfaces.

In the above figure :

At sharp points (small radius of curvature), the perpendicular component of electric repulsion ( $\displaystyle \left| {{\overrightarrow{F}}_{\bot }} \right|$ ) is greater than the parallel component ( $\displaystyle \left| {{\overrightarrow{F}}_{\parallel }} \right|$ ). As a result, charged particles stay closer together, leading to higher surface charge density.
At flatter regions (large radius of curvature), the parallel force dominates ( $\displaystyle \left| {{\overrightarrow{F}}_{\parallel }} \right|$ ), causing charges to spread farther apart, which results in lower surface charge density.

Above concept of more surface charge density at sharp points can also be explained on the basis of radius of curvature. Since behave as equipotential surfaces, so potential at every point of a conductor is same. V = constant. Now if r_c is the radius of curvature of an part of the conductor, then electric potential is given by :

$\displaystyle V=\frac{kq}{{{r}_{c}}}=constant$