Education Journalist | Study Abroad Lead
Electrostatics of conductor is zero in static condition. For a charged conductor, the charges will lie on the surface of the conductor. Thus, there will not be any charges inside the conductor. When there is no charge there will not be electric field. A conductor is a material which conducts electricity from one place to the other. Conductors have loosely bound electrons to allow current to flow.
Also read: Electrostatic Potential and Capacitance
Key Terms: Metallic conductors, Induced electric field, Electric field lines, Gauss law, Electric field, Potential, Electric flux, Surface charge density
Electric Field Inside a Conductor
[Click Here for Sample Questions]
Suppose a conductor is in the external electric field Eo. Since it is a conductor, the free electrons move to the left side because of the electric field Eo. As a result, some negative charge appears on that side. These are known as induced charges. Similarly, a net positive charge appears on the right side.
These charges produce an induced electric field Ep inside the conductor which opposes the flow of free electrons from right to left. The flow, therefore, stops as soon as Ep becomes equal to Eo. When the applied electric field and the induced electric field become equal, which happens instantly, the net electric field in the interior of the conductor is zero.
So the net electric field inside the onductor is zero in the absence as well presence of external electric field.
Electric Field Inside a Conductor
Read More: Characteristics of a Transistor
Interior of Conductor
[Click Here for Sample Questions]
Suppose we have a random volume element V inside a charged conductor. Let us call the closed surface S bounding this volume. On this closed surface S, the electrostatic field is zero as we know the net electric field inside a conductor is zero.
Since the electric field is zero, so by Gauss’s law the net charge enclosed is also zero. Since V is an arbitrary volume, so it can be made as small as possible. Thus, there is no net charge at any point inside the conductor. So if any charge is given to the conductor, it will always reside on the surface.
Also Read:
Electrostatic Field Lines
[Click Here for Sample Questions]
Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. The flow of charges on a conductor stops after the charges are rearranged. That means all charges get static. This implies that the component of electric field tangent to the surface of the conductor must be zero.
i.e. E cosx = 0, x is the angle which electric field intensity makes with tangent to the surface
As E cannot be equal to zero, as there is charge on the surface. Therefore,
Cosx = 0 or x = \(90^{\circ}\)
Hence electric field lines are always perpendicular to the surface. The direction depends on the type of charge. Electric field lines are always directed from positive to negative charge. So if the surface is positively charged. Electric field lines will be normally outward and if negatively charged electric field lines will be radially inward.
Also Read:
| Related Articles | ||
|---|---|---|
| Equipotential Surface | Derivation of Potential Energy | Van de Graaff Generator |
Electrostatic Potential
[Click Here for Sample Questions]
Electric field inside the conductor is zero, so no work is done in moving a small test charge within the conductor. Therefore, the potential difference between any two points inside the conductor is zero. This implies that electrostatic potential is the same throughout the volume of the conductor.
Electric field is perpendicular to the surface of the conductor. As explained before, the electric field has no tangential component on its surface. So electrostatic work done will be zero in moving a test on the surface of the conductor. This implies potential difference will be zero between any two points on the surface of the conductor. Hence, electrostatic potential is constant everywhere, inside as well as on the surface.
Also read: Capacitance Formula
Surface Density of Charge
[Click Here for Sample Questions]
Surface Density of Charge
Consider a short cylinder of small area of cross section ds and negligible height partly immersed and partly outside the surface of a conductor of surface charge density σ as shown in the figure.
We know, inside the surface E = 0
Just outside the surface the field E is normal. The outer circular cross section of the cylinder only contributes to the total flux through the cylinder. Over the small area ds, take E to be constant, electric flux = ± E ds, positive for σ > 0 and negative for σ < 0.s
As charge enclosed by the element = σ ds
Therefore, by Gauss’s theorem E (ds) = σ dsϵo or E = σ ϵo
As electric field is always normal to the surface, E = σ ϵo ^n
This equation is true for both signs of σ.
Surface Charge Density is Different at Different Points
If we place a conductor in an electric field, the negatively charged particles, that is electrons, rearrange themselves so that the potential on the entire surface remains the same. This makes the local charge density σ (charge per unit area) different at different points on the surface of the conductor.
Charge density will be positive where the charge is positive and negative at areas where the charge on conductor is negative. Further, at small areas or where the radius of curvature is smaller, at that points charge density is higher and vice-versa.
Surface Charge Density
Things to Remember
- Inside a conductor electric field is zero
- There is no static charge inside the conductor
- Electric field lines are always perpendicular to the surface, no matter what charge it is
- Electrostatic potential has same value everywhere on the surface as well as inside the conductor
- Charge per unit area (σ) can be different at different point on the surface of the conductor
- On applying an external electric field, a field is induced inside the conductor called induced electric field
- Charges on the surface of the conductor remains static unless external force is applied in them
Read More:
Sample Questions
Ques. Why are metals said to be good conductors of electricity? (2 Marks)
Ans. In metals, the valence electrons are loosely bound to the atoms. So even at room temperature they are free from the influence of the nucleus and therefore free to move. This free movement of electrons at room temperature gives them flow freely and hence leading to high conduction current. Plus, the hindrance to flow of electrons in metals is quite low as the vibration of fixed atoms at room temperature is quite low.
Question 3: Faraday entered a big metallic cage which is placed on insulating pillars and then charged the cage. He remained quite safe inside the cage. Justify the concept. (2 Marks)
Ans. Yes. As the cage is insulated, the entire charge remains on the surface of the cage. The potential at all points inside the cage remained the same. As there was no potential difference between any two points in the cage, Faraday could not get the shock and remained quite safe inside the cage.
Ques. The safest way to protect yourself from lightning is to be inside a car. Comment. (2 Marks)
Ans. The body of the car is metallic. It provides electrostatic shielding to the person in the car, because as we know the electric field inside the conductor is zero. So the charge and field stay on the surface of the car and pass to the ground through the metallic body of the car.
Ques. Can ever the whole charge of a body be transferred to the other? Explain. (2 Marks)
Ans. Yes, the whole charge of a body X can be transferred to body Y, when X is enclosed in Y and is connected to it by metallic wire. This is because charge always resides on the outer surface of the conductor.
Charge of Body
Ques. A sensitive instrument with an electrostatics of conductor is to be shifted from a strong electrostatic field in its environment. Suggest a possible way. (2 Marks)
Ans. For this, the instrument must be enclosed fully in metallic cover. This will provide electrostatic shielding to the instrument. So when the instrument is moved, it will have no effect on the electric field as the field can only reside on the surface of a conductor.
Ques. During lightning, you are safer inside a house than under a tree. Why? (2 Marks)
Ans. When we stand under a tree, there is no resistance to lightning, so we give it an easy path to pass through our body. But when we are in the house, current due to the lightning is conducted to the ground through iron pipes or walls. Hence, we are safer in a house.
Ques. Why does a charged glass rod attract a piece of paper? (2 Marks)
Ans. Paper is a dielectric. When a positively charged glass rod is brought near it, atoms of paper get polarized, with the center of negative charge of atoms coming closer to the glass rod. The force of attraction between paper and glass rod becomes greater than the force of repulsion. So the positively charged glass rod attracts the piece of paper.
Ques. Can charge density be equal at all points on the conductor? Explain. (2 Marks)
Ans. It depends on the shape of the conductor. Since the conductor follows the tendency to make electrostatic potential equal at all points on its surface, the charge carriers arrange themselves accordingly. Due to this charge densities can be different at different points. If however, the conductor is symmetrical in space, such as that sphere, then the surface charge density is constant at all points.
Ques. Explain why the electric field inside the conductor is zero? (3 Marks)
Ans. When an external electric field is applied to a conductor, polarities develop on its both ends. These polarities give rise to internal electric fields. This internal electric field keeps getting stronger until the charges inside the conductor keep arranging themselves.
When the charges stop moving, the electric field inside the conductor becomes equal to the outside of the conductor, but opposite in direction. Due to this they get cancelled and the net electric field inside the conductor becomes zero.
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Check-Out:
Comments