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Electric displacement, which is denoted by D, is the charge per unit area that would be displaced across a layer of conductors placed across an electric field. It is also known as electric flux density. Electric displacement finds its application in the dielectric material to find the response of the materials to the application of an electric field E. The SI unit of electric displacement is Coulomb per meter square (C m-2). Here we will be learning more about electric displacement and discussing some important questions.
| Table of Content |
Key takeaways: Electric displacement, dielectric material, vacuum permittivity, polarization density, a vector quantity, coulomb, electric field, electric flux
Read Also: Electrostatic Potential and Capacitance Important Questions
What is Electric Displacement?
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The displacement of electric charge across a conductor in an electric field is referred to as electric displacement. It essentially measures the charge per unit area and is also known as electric flux density. As a result, it only applies to free electric charges, excluding the participation of charges found in molecules or neutral atoms. It works primarily because when a charge travels between two uncharged conductors, an electric field forms between them. As a result, one conductor has a positive charge, whereas the other has a negative charge. This results in the formation of an electric field between these conductors. As a result, the goal of this idea is to determine the free charge surface density. Furthermore, it refers to the volume of free charge on one conductor in relation to the surface area of this conductor.
Read more: Unit 1 Chapter 2 Electrostatic Potential and Capacitance
Equation of Electric Displacement?
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First and foremost, the letter ‘D' stands for electric displacement. 'E,' on the other hand, refers to the electric field that is involved in the equation. The electric displacement equation can be represented as:
| D = ε0E + P |
Where,
- ϵ0: Vacuum permittivity
- P: Polarization density
- E: Electric field
- D: Electric displacement field
Its SI unit is C m-2, which stands for Coulomb per meter square. Coulomb is the unit of electric charge in this unit, and m-2 is the material's area. You need also to understand what vacuum permittivity and polarisation density mean. It will help you better grasp the elements at work in the phenomena. Vacuum permittivity is a physical constant that refers to an electric field's capacity to permeate a vacuum. However, it is a relationship between the units of electric charge and force. Length is also an important aspect of this notion. It has the value 0 = 1/0c2. In this example, 0 denotes the magnetic constant, and c denotes a constant value of 299,792,458 m s-1.
What is Dielectric Material?
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A dielectric material can be referred to as an electrical insulator such that when an electric field is applied it can be polarized. When placed in an electric field there is no flow of electric charges, but they do move from their average equilibrium position resulting in dielectric polarization. These materials can be used in capacitors, radios, and transmission lines for radiofrequency. The dielectric material in a capacitor is given as:
| C = εrε0A/d |
Where,
- C: Capacitance
- ϵ0: Vacuum permittivity
- ϵr: Relative permittivity of the material
- A: Area of the plates used in the capacitor
- d: Distance between the plates
Read more: Difference between Capacitor and Battery
What is Vacuum Permittivity?
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Vacuum permittivity can be described as the value of absolute dielectric permittivity. Meaning, that it is the capability of the vacuum to permit electric field lines. The approximate value and formula of vacuum permittivity which is represented by ϵ0 are as follows:
| ϵ0 = 8.854187 …*10-12 F.m-1 |
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What is Polarization Density?
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A vector field describing the density of dipole moments in a dielectric object. As previously mentioned, the entrance of such an item into an electric field causes charges to migrate. It is the electric dipole moment that polarises a certain item. As a result, polarisation density determines the electric dipole moment per unit volume of dielectric material.
| P = △p/△V |
- P: polarisation density
- Δp: dipole moment
- ΔV: volume element
How does it work?
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The density of electric flux within a charged field is therefore calculated using electric displacement. It does, however, take into consideration the case where a dielectric is introduced into the device. It is important to understand that a dielectric is an insulating substance that does not include any free or loosely bound electrons.
As a result, they do not require the passage of free electric charges throughout their surface area. When an insulated item is placed between an electric field, it experiences some polarisation. Because the tightly bonded negative charges migrate somewhat towards the positive conductor, this occurs.
Bound positive charges, on the other hand, migrate to a considerable extent towards the negative plate. The total electric field decreases as a result of this occurrence. As a result, electric displacement investigates the responses of dielectric materials when they come into contact with electric fields.
Work of Electric Displacement
Read more: Magnetic Field in A Solenoid Formula
How is Electric Displacement a Vector Quantity?
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When a dielectric substance is placed in an electric field, it causes a change in the electron cloud of free electrons. As a result, it is referred to as a dipole. The dielectric's negative and positive charges have an attraction for positive and negative plates, respectively. As a result, they go along a specified line in precise directions. The dielectric polarization vector is thus measured via the electric displacement vector.
As a result, the vector flow of electric density in a particular dielectric material is measured by electric displacement density. Coulombs per metre square, or C m-2, is the unit in the meter-kilogram-second system.
Things to Remember
- One conductor has a positive charge, whereas the other has a negative charge. This results in the formation of an electric field between these conductors. As a result, the goal of this idea is to determine the free charge surface density.
- The equation for calculating electric displacement in a dielectric medium is - D = ε0E + P
- The density of electric flux within a charged field is therefore calculated using electric displacement.
- It essentially measures the charge per unit area and is also known as electric flux density.
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Sample Questions
Ques: What is electric displacement? (1 mark)
Ans: The displacement of electric charge across a conductor in an electric field is referred to as electric displacement. It essentially measures the charge per unit area and is also known as electric flux density.
As a result, it only applies to free electric charges, excluding the participation of charges found in molecules or neutral atoms. It works primarily because when charge travels between two uncharged conductors, an electric field forms between them.
Ques: What is the equation for electric displacement? (2 mark)
Ans: you should look at the following table to comprehend the other components of this equation –
| ε0 | Vacuum Permittivity; |
| P | Polarization Density |
As a result, the equation for calculating electric displacement in a dielectric medium is -
D = ε0E + P
Ques: A 500 C charge is located in the centre of a 10 cm square. Calculate the effort required to move a charge of 10 C between two diagonally opposed spots on the square. (1 mark)
Ans: It is because these two locations are at equipotential, the effort done in transferring a charge of 10 C between two diagonally opposed places on the square is zero.
Ques: A solitary charge as indicated in the diagram, Q is positioned at point O. If Q is positive (ii) negative, is the potential difference VA – VB positive, negative, or zero? (2 mark)
Ans: As,
OA OB, the quantity within the bracket is negative.
I If q has a positive charge, VA – VB equals negative (ii) If q has a negative charge, VA – VB equals positive.
Ques: What is an electric displacement vector? (3 marks)
Ans: The electric displacement field, which is denoted by D, or electric induction is a vector field that appears in Maxwell's equations. The electric displacement vector accounts for the effects of free and bound charges within materials. "D" stands for "displacement", as in the related concept of displacement current in dielectrics.
Ques: What is meant by electric displacement and flux density? (3 marks)
Ans: Electric displacement (D), also known as electric flux density, is the charge per unit area that would be displaced across a layer of conductor placed across an electric field. This describes also the charge density on an extended surface that could be causing the field.
Ques: What is meant by electric displacement in the capacitor? (3 marks)
Ans: The electric displacement, usually denoted by its first letter D and also known as dielectric displacement, is a vector field in a non-conducting medium, a dielectric. The displacement D is proportional to an external electric field E in which the dielectric is placed.
Ques: Why is electrostatic potential constant throughout the volume of the conductor and has the same value (as inside) on its surface? (1 mark)
Ans:
Electric field inside the conductor = 0
\(E=-\frac{dV}{dr} \implies \frac{dV}{dr}=0 \therefore \textbf{V=Constant}\)
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