Table of Contents
Introduction:
Electric field:
An electric field is an electric property that is associated with every location in space where a charge exists in any form. The electric force per unit charge is another term for an electric field.
The electric field formula is as follows:
E = F /Q
Where,
The electric field is denoted by the letter E, F is force, the charge is Q.
Variable magnetic fields or electrical currents are the most common causes of electric fields. The volt per metre (V/m) is the SI unit for measuring electric field strength. The direction of the field is regarded as the direction of the force that would be exerted just on a positive charge. A positive charge produces a radially outward electric field, while a negative charge produces a radially inward electric field.
A brief outline:
How to Use Gauss Law to Determine Electric Field:
There are some steps that should be followed.
- To begin, we must determine the charge distribution’s spatial symmetry (spherical, cylindrical, or planar).
- The next step is to identify a gaussian symmetry that is identical to the symmetry of the spatial arrangement.
- Find the flow by finding the integral along the gaussian surface.
- Charge encapsulated by a Gaussian surface should be found.
- Determine the charge distribution’s electric field. A point charge produces an electric field.
The electric field seems to be a vector field that is connected with the Coulomb force that a test charge experiences at each point in space relative to the source charge. The Coulomb force F on the test charge q can be used to calculate the magnitude and direction of the electric field. The electric field formed by a positive charge will be radially outwards, while the electric field created by a negative charge will be radially inwards.
Important concepts:
An infinite, uniformly charged sheet:
The total electric flux across a circular area holding charges is calculated using Gauss’s law, which divides the charge by the permittivity of empty space. We have had the Gaussian surface as well as the charged sheet in this case. We can find the total charge encompassed by the surface by determining the location of the charged sheet within the gaussian sphere now that we have the surface charge density. The total electric flow can then be calculated using Gauss’s law.
The all-out electric transition through a shut surface is equivalent to the absolute charge encased by the surface partitioned by the permittivity of open space, as per Gauss’ hypothesis.
The proportion of electric field lines going through a specific surface ordinary to the electric field is known as electric transition. We can numerically address Gauss’ regulation as follows:
Φ=Qε0
Where Φ is the electric flux, Q is the total contained charge, and ε0 is the free space permittivity.
We will use Gauss’s law to calculate the electric flux through the given surface in the provided question.
The total charge encompassed by the gaussian surface must be determined.
The sheet’s charge density is σ.
The gaussian surface will enclose a circular portion of the sheet. The circular sheet’s radius will be,
a= √ R²−x²
As a result, the circular sheet’s area within the gaussian sphere would be,
A=πa² =π(R²−x²)
The charge that the gaussian surface encloses is,
Q=σA
Q=π(R²−x²) σ
Φ=Q/ε0
=π(R²−x²) σ/ε0
The area integral of the electric field over every closed surface equals the total charge encompassed by the surface divided by the permittivity of free space is the integral version of Gauss’s law. It can be expressed numerically as,
∫E→ .d A→ = Q/ε0
Infinite sheets are almost hard to create, however a point near a finite sheet can be considered as if it were near an infinite sheet, and the same approach can be used. Similar issues will be thoroughly addressed in capacitors. Because the sheet is conductive, the electric field is half that of a typical infinite sheet. The conducting sheet’s plane must be intersected by the Gaussian surface. The electric field is determined solely by the charge density and surface area, and the electric constant.
The Gaussian surface is a closed surface in three-dimensional space that can be used to compute the flux of a vector field. The gravity field, electric field, or magnetic field all are instances of vector fields. Gaussian surfaces can be calculated using Gauss’ law:
Gaussian Surface Formula:
Where Q(V) is the electric charge contained in the V.
ΦE= ∫∫E .d A = Q(V)/ε0
Electric field lines:
These are really a great way to see how electric fields look. Michael Faraday was the one who originally introduced them. At a location, a field line is drawn tangential to the net. As a result, the tangent to the electric field line at any place corresponds to the presence of an electric field at that location. Second, the relative density of field lines surrounding a point reflects the strength (magnitude) of an electric field at that location. In other words, if there are any more electric field lines in the area of point A than there are in the vicinity of point B, the electric field at point A is stronger.
Electric Field Line Properties:
The field lines seldom cross one another. The field lines run perpendicular to the charge’s surface. Both the amount of the charge, as well as the number of field lines, are proportional. The field lines begin with the positive charge and conclude with the negative charge. A single charge should be used to start or finish the field lines at infinity. Drawing Electric Field Lines: Rules The rules for designing electric field lines are as follows: The field line starts at the charge and continues at infinity or at the charge. The field lines are nearer together as the field is stronger. Depending on the charge, the number of field lines varies. Crossing the field lines is never a good idea. At the point where they pass through, the electric field and applied electric line are tangent.
Significance of Gauss’s law in NEET exam:
Physics is devoted to the study of an endless evenly charged sheet. All of these topics are covered by the NEET test. The NCERT Physics textbook, which was created specifically for the NEET test, goes through them in depth. By visiting the infinite learn website, students can learn about such concepts as well as the derivation of various formulas connected to them. There are also several issue problems in the chapter’s tasks to help you practice and grasp the topic’s application. Students could also study physics textbooks from other publishers.
Infinity Learn offers a wide range of resources to assist students in learning each subject in a structured manner. Students can also learn much more about the subject by using the self-study materials provided. There are sample question sets available that can be used to practice additional questions and improve test preparation. Any student can receive access to these resources by registering on the website, which is entirely free. The remaining study guides can also be downloaded for free.
Frequently asked questions (FAQ):
Question 1. What is a Gaussian Pillbox, and how does it work?
Answer: The electric field is calculated using the Gaussian pillbox, which is a surface with an infinite charge and uniform charge density. The pillbox has a cylindrical shape and is made up of three parts: a disc with an area of Пr4, a disc with an equal area at the other end, and the cylinder’s side. The sum of electric flux through each element is proportional to the contained charge of the pillbox, according to Gauss law.
Question 2. Between plates a and b, there is a uniform electric field e, and between plates c and d, there is a uniform magnetic field b.
Answer: Between plates a and b, there is a uniform electric field e, and between plates c and d, there is a uniform magnetic field b. A rectangular coil X moves between AB and CD at a constant speed, with its plane aligned to the plates. When the coil enters and exits CD, it generates an emf.
Question 3. The mean velocity of free electrons in a conductor at actual temperature (T) in the lack of an electric field is
Answer:
- When there is no electric field
- The electron travels in a zig-zag pattern.
- The mean velocity of free electrons in a conductor at absolute temperature is zero because the net displacement is zero.
