According to Gauss’s Law, the total electric flux (equation below) across a Gaussian surface is equal to the charge enclosed by the surface divided by the permittivity of free space.
The electric flux of the sphere is also referred to as the product of the electric field and the surface area of the Gaussian surface.
- Q = Total charge on our sphere
- r = Radius of the sphere
- A = Surface area of a sphere (4πr2)
- E = Electric Field due to a point charge Q/ 4επr2
- ε = permittivity of free space (constant)
Table of Contents
What is Sphere?
A sphere is symmetrical and round in form. It is a three-dimensional solid with all of its surface points at equal distances from the centre. Based on its radius, it has surface area and volume. It lacks any faces, corners, or edges.
Electric Field
An electric field (E.F) is a field or space that occurs around an electrically charged particle and in which another test charge feels an attractive or repulsive force. An E.F. is also defined as an electric property associated with a specific location in space when a charge is present.
Electric Field Strength
The electric or Coulomb force F exerted per unit positive electric charge q at that place, or simply E = F/q is used to characterize the strength of an electric field at a certain location. It is a vector quantity, which implies it has a magnitude as well as a direction. Its equation is as follows:
Where F = force acting in newtons and q = charge in coulombs.
Electric Field of a Point Charge
Consider that we have a source charge that is placed in the vacuum. A second test charge (q) is positioned r away from the source charge.
The force acting on the test charge is as follows:
The E.F induced around the source charge is given by the following
Electric Field of Sphere- Key Points
- The electric field of a sphere is a product of the electric field and the surface area of the Gaussian surface.
- E.F. units are volts per meter (V/m) and Newtons per coulomb.
- The electric force is the net force on a small, imaginary, and positive test charge.
- E.F. arrows point out of positive charge and into negative charge.
- The E.F. is radially outward from the point charge in all directions.
- Electric field lines are always perpendicular to the source and the terminal. They come out perpendicularly from the positive surfaces and enter perpendicularly to the surfaces that are negative.
Electric Current
Electric current is the rate at which negative charges flow through a conductor (current electric).
To put it another way, an electric current is the continuous movement of electrons in an electric circuit. The conducting material is composed of a huge number of free electrons that flow randomly from one atom to the next.
Electromagnetic Force
When a conductor is placed in a magnetic field and current is passed through it, the magnetic field and current interact to produce force. This force is referred to as Electromagnetic force. Fleming’s left-hand rule determines the direction of the current, magnetic force, and flux.
The properties of electromagnetic force are as follows:
- The inverse square law applies to electromagnetism.
- In nature, it may be both attractive and repellent.
- It is a long-distance force.
- The photon is an electromagnetic force field particle.
An electromagnet is a magnet that uses an electric current to produce a magnetic field. The magnetic field vanishes when the current is switched off.
Electromagnetic Force Formula
The Lorentz force refers to the total electromagnetic force F acting on a charged particle and its equation is as follows:
 | = | force |
 | = | electric charge |
 | = | external electric field |
 | = | velocity |
 | = | magnetic field |
Important Links
Magnetic field | Definition & Facts | Britannica
Electric Current Definition and Explanation
Malus Law- Definition, Concept, and Examples
Bottom Line
The electric field of a sphere of uniform charge is a measure of the electric force that acts on a test charge placed at a particular point in space relative to the charged sphere. The electric field is a vector quantity that describes the direction and magnitude of the electric force.
In the case of a sphere of uniform charge, the electric field at any point outside the sphere can be calculated using Coulomb’s law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
For a sphere of uniform charge, the electric field is proportional to the charge density of the sphere and inversely proportional to the square of the radial distance from the centre of the sphere to the point where the electric field is being calculated. The electric field inside the sphere is zero.
In summary, the electric field of a sphere of uniform charge describes the distribution of electric force around the sphere and helps to understand how the charged sphere interacts with other charged objects in its vicinity.
Frequently Asked Questions
1. What is Biot Savart Law?
The Biot Savart Law is a mathematical formula that defines how a continuous electric current produces a magnetic field. It relates the magnitude, direction, length, and closeness of the electric current to the magnetic field. Biot–Savart’s law is compatible with both Ampere’s circuital law and Gauss’s theorem.
2. What is the Potential Difference?
The potential difference between two places in a circuit is the difference in the amount of energy that charge carriers have. The quantity of current multiplied by the resistance equals the potential difference (also known as voltage).
3. What is Direct Current?
Direct current is the unidirectional flow of electric charge (DC). In electrical engineering, the word DC refers to power systems that have just one polarity of voltage or current and a constant, zero-frequency, or slowly changing local mean value of voltage or current.
4. What’s Alternating Current?
The flow of electrons in an alternating current (AC) changes direction at regular intervals or cycles. Power lines carry alternating currents, and traditional home electricity comes from a wall outlet.
5. What is surface charge density?
Surface charge density (σ) is the amount of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a two-dimensional surface charge distribution.
6. What is ampere’s law?
According to Ampere’s law, the integral of magnetic field density (B) along an imaginary line is equal to the product of free space permeability and current enclosed by the path.
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