# Electrostatic Conductor

## What is a Conductor?

An object or a type of material that allows the flow of charge in one or more directions is known as a conductor. Common electrical conductors are materials made up of metal. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and in some cases positive or negative ions.

It is not necessary for one charged particle to travel from the machine producing the current to that consuming it for the current to flow. To power the machine, the charged particle simply needs to nudge its neighbor a finite amount who will nudge its neighbor until a particle is nudged into the consumer.

### Coulomb’s Law of Electrostatics

We begin with the magnitude of the electrostatic force between two point charges q and Q. We can conveniently label one of these charges, Q a source charge and label q, as a test charge. If r is the distance between two charges, then the force of electrostatic formula is:

$F = \frac{1}{4 \pi \epsilon_{0}} \frac{qQ}{r^{2}} = k \frac{qQ}{r^{2}}$

$F = k\frac{q_{1}q_{2}}{d^{2}}$.

### Electrostatic Properties of a Conductor

• The Electrostatic Field is Zero Inside a Conductor:

In the static condition, a conductor neutral or charged, the electric field inside the conductor is zero everywhere, this is also one of the primary properties of a conductor. In the presence of an electric field, we know that the free electrons which a conductor contains, experiences a drift or a force. The electrons distribute themselves in such a way Inside the conductor that the final electric field is zero at all points inside the conductor.

• At the Surface of the Charged Conductor Electric Field is Perpendicular to the Surface:

If the electric field lines were not normal at the surface, then we can say that a component of the electric field would have been present along the surface of a conductor in static conditions.. Since there are no tangential components, the forces have to be normal to the surface.

• In the Static Condition, the Interior of the Conductor Contains no Excess Charge:

At every point, any neutral conductor contains an equal amount of positive and negative charges, even in an infinitesimally small element of surface area or volume. From Gauss’s law we can say that in case of a charged conductor, the excess charges are present only on the surface. Consider, any arbitrary volume element of the conductor, denoted as ‘v’, and the electrostatic field is zero for the closed surface bounding the volume element. The total electric flux through S is therefore zero. From the Gauss law, it signifies that the net charge enclosed by the surface element is zero.  At a point, we can say that the element is vanishingly small,  it denotes any point in the conductor as we go on decreasing the size of the volume and the surface element. So the net charge inside the conductor is always zero at any point and the excess charges reside at the surface.

• Throughout the Volume of the Conductor Electrostatic Potential is Constant:

Throughout the volume of the conductor, the electrostatic potential at any point is always constant and at any point inside the volume, the value of the electrostatic potential at the surface is equal to that.

### Fun Facts

• Free charges are allowed to move about within a conductor.

• Until static equilibrium is reached, free charges are caused to move around inside the conductor by the electrical forces around a conductor.

• All excess charges are collected along the surface of a conductor.

• More charges can be collected at the points of the conductors which has a sharp corner or point.

• A lightning rod is a conductor with sharply pointed ends that allows the excess charge to dissipate back into the air collected on the building caused by an electrical storm.

• Due to changes in the insulating effect of the air, the electrical field of Earth’s surface in certain locations becomes more strongly charged and results in electrical storms.

• A Faraday cage acts as a shield around an object, preventing the electric charge from penetrating inside. Faraday cage is a metal shield which prevents electric charge from penetrating its surface.

1. Consider an Arbitrary Electric Field Configuration. a Little Test Charge is Placed at a Null Point (i.e., where E = 0) of the Configuration. Display that the Equilibrium of the Test Charge is Necessarily Unstable?

Suppose if the equilibrium of the test charge is stable. If the given test charge displaced from its position in any direction and is in equilibrium, then further it experiences a restoring force towards a null point, where the electrical field is zero. All the sector lines near the null point are directed inwards towards the null point. there's a net inward flux of electric field through a closed surface around the null point. consistent with Gauss's law, the flux of the electrical field through a surface, which isn't enclosing any charge, is zero. Hence, the equilibrium of the test charge is often stable.

2. A Hollow Charged Conductor Features a Tiny Hole dig its Surface. Show that the σ/2ε₀ n̂, where n̂ is that the Unit Vector Within the Outward Normal Direction and σ is that the Surface Charge Density near the Opening.

Let us consider a conductor with a cavity or a hole. The field inside the cavity is zero.

Let E is that the field just outside the conductor, q is that the charge, σ is that the charge density and ε₀ is that the permittivity of free space.

Charge q = σ x ds

According to Gauss’s law, flux, 𝜙 = E . ds = q/ε₀

⇒ E . ds = σ x ds/ε₀

E = σ/2ε₀ n̂

Therefore, the electrical field just outside the conductor is σ/2ε₀ n̂. This field may be a superposition of field thanks to the cavity E’ and therefore the field thanks to the remainder of the charged conductor E’. These fields are opposite and equal inside the conductor and equal in direction and magnitude outside the conductor.

E’ + E’ = E

E’ = E/2 = σ/2ε₀ n̂

Hence, the sector thanks to the remainder of the conductor is σ/2ε₀ n̂.