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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

The figure shows the effect of an external electric field on a free positive charge near the surface of a conductor. (Equivalently, free electrons would move in the opposite direction.) If the electric field has a component parallel to the conductor’s surface, it exerts a force on the free charges and causes them to move along the surface. This redistribution of charge continues until electrostatic equilibrium is established.

In electrostatic equilibrium, there can be no component of the electric field parallel to the conductor’s surface. If such a component existed, it would continue to exert a force on the free charges and produce further motion. Therefore, the tangential (parallel) component of the electric field must be zero, and the resultant electric field is perpendicular (normal) to the surface of the conductor.

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

The process of protecting a certain part from the effect of an electric field is called electrical shielding or electrostatic shielding. Conductors can act as electrostatic shields. Since the electric field inside a conductor is zero, sensitive equipment’s can be protected from external electric fields by placing them within a conductive cage (such as a Faraday cage). This is why sitting in a car when lightning strikes is safer than sitting under a tree or in an open field.

5. Conductors Behave as Equipotential Surfaces

Since the electric field inside a conductor is zero ( $\displaystyle \overrightarrow{{{E}_{in}}}=0$ ) and there is no component of the electric field parallel to the surface of the conductor ( $\displaystyle \overrightarrow{{{E}_{\parallel }}}=0$ ), no work is required to move a charge either inside the conductor or along its surface.

$\displaystyle {{V}_{B}}-{{V}_{A}}=\frac{{{W}_{AB}}}{q}=\frac{0}{q}=0$

$\displaystyle \Rightarrow {{V}_{B}}={{V}_{A}}$

That is,

Electric Potential (V) = Constant

Hence, the electric potential remains constant throughout the conductor and on its surface, irrespective of the conductor’s size, shape, and charge distribution.

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. Applying Gauss’s law inside the conductor,

$\displaystyle \phi =\oint{\overrightarrow{{{E}_{in}}}}.\overrightarrow{dS}=\frac{{{q}_{in}}}{{{\varepsilon }_{0}}}$

However, we know that the electric field inside a conductor is zero ( $\displaystyle \overrightarrow{{{E}_{in}}}=0$ ), Therefore,

$\displaystyle \frac{{{q}_{in}}}{{{\varepsilon }_{0}}}=\oint{\overrightarrow{{{E}_{in}}}}.\overrightarrow{dS}=0$

$\displaystyle \Rightarrow {{q}_{in}}=0$

Thus, in electrostatic equilibrium, no excess charge can exist inside a conductor. If any excess charge is present, it must reside entirely on the surface of the conductor.

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 conductors 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 :

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