Ellipse: Do you know the orbit of planets, moon, comets, and other heavenly bodies are elliptical? Mathematics defines an ellipse as a plane curve surrounding...

Ellipse: Definition, Properties, Applications, Equation, Formulas
April 14, 2025Harvest Smarter Results!
Celebrate Baisakhi with smarter learning and steady progress.
Unlock discounts on all plans and grow your way to success!
Ellipse: Definition, Properties, Applications, Equation, Formulas
April 14, 2025Altitude of a Triangle: Definition & Applications
April 14, 2025Manufacturing of Sulphuric Acid by Contact Process
April 13, 2025Refining or Purification of Impure Metals
April 13, 2025Pollination and Outbreeding Devices: Definition, Types, Pollen Pistil Interaction
April 13, 2025Acid Rain: Causes, Effects
April 10, 2025Congruence of Triangles: Definition, Properties, Rules for Congruence
April 8, 2025Complementary and Supplementary Angles: Definition, Examples
April 8, 2025Nitro Compounds: Types, Synthesis, Properties and Uses
April 8, 2025Bond Linking Monomers in Polymers: Biomolecules, Diagrams
April 8, 2025The electrons in a conductor are. charge carriers would feel force and drift as long as the electric field is not zero. The charges distribute themselves so that the electric field is zero everywhere inside the conductor when there is no current inside or on the surface of the conductor. Inside a conductor, the electrostatic field is nil.
Now talking about the electric potential due to charged solid sphere, let us consider a charged sphere that has a symmetrical charge distribution. The electric field outside the sphere, according to Gauss’ Law, is the same as that produced by a point charge. This means that the potential outside the sphere is the same as the potential from a point charge. Consider a solid insulating sphere with a radius R and a charge distributed uniformly throughout its volume. Both the electric field and the electric potential outside the sphere are identical to the field and potential from a point charge.
When Gauss’ law is applied to the electric field of a charged sphere, the electric field environment beyond the sphere is found to be similar to that of a point charge. As a result, the potential is identical to that of a point charge:
Because the electric field inside a conducting sphere is zero, the potential at the surface remains constant:
The voltage inside a conductor at equilibrium is bound to be constant at the value it achieves at the conductor’s surface because the electric field is equal to the rate of change of potential. The charged conducting sphere serves as a nice illustration, but the idea is valid for all conductors in equilibrium.
In the sphere itself, what about it? We know the field within the sphere is zero if it is a conductor. What about its potential? The potential varies by an amount when one moves from a point on the outside to a location inside the sphere:
ΔV = -∫ E • ds
Given that E = 0, we can only infer that V is also zero, meaning that V is constant and equal to the potential at the sphere’s outer surface.
What takes place within the sphere? Due to the presence of a field inside the sphere, the potential is no longer constant. We demonstrated using Gauss’ Law that the field within an evenly charged insulator is as follows:
E =k Q r/R3
If all of the charge inside the sphere were concentrated at its centre, it would have the same potential as the vacuum at that place if it were conducting. To understand this, first note that the conducting sphere is a surface that must necessarily be equipotential. It follows that the field outside the sphere is radial and inverse-square just as if the charge had been at the centre due to the uniqueness of solutions to Laplace’s equation.
Applying Gauss’s formula now outside the sphere reveals that the electric field’s strength must be ?/4??0?2 because the total enclosed charge is merely the sphere’s internal charge. Integrating from infinity results in the same potential, ?/4??0?, because the electric field outside the sphere is the same as the one produced by a single charge Q at the centre without a conducting shell. Keep in mind that this reasoning is independent of the charge’s location within the sphere.
If the sphere is not conducting, the potential at the sphere will be determined by the conventional formula, ?/4??0? , where d is the separation between the charge and the specific point on the sphere. Keep in mind that the charge’s placement in this scenario is important; if the charge is not in the centre, the sphere will not be an equipotential surface. The volume of an infinitely thin shell is zero, hence its polarisation has no bearing on anything, regardless of whether the sphere is a dielectric or not.
We hope this short article on Electric Potential Due To Charged Solid Sphere has been helpful. Stay tuned to Embibe for such informative articles. Happy learning!
Ellipse: Do you know the orbit of planets, moon, comets, and other heavenly bodies are elliptical? Mathematics defines an ellipse as a plane curve surrounding...
Altitude of a triangle is the side that is perpendicular to the base. A triangle has three sides altitude, base and hypotenuse. The altitude of...
Manufacturing of Sulphuric Acid by Contact Process: Sulphuric acid is referred to as the king of chemicals. It is one of the most important chemical...
Refining or Purification of Impure Metals: Metals like Copper, Aluminium, Iron, etc., occur in nature in the combined state, in the form of their oxides,...
Pollination and Outbreeding Devices: Flowers are symbolic of beauty and have aesthetic, ornamental, social, religious and cultural value. But how are they formed? Let us...
Congruence of Triangles: The congruence of a triangle depends upon the measurements of sides and angles of the two triangles. There are a few criteria,...
Complementary and Supplementary angles are defined for the addition of two angles. If the sum of two angles so formed is \({90^ \circ }\), then...
Nitro compounds are a group of organic compounds having Nitro group \({\rm{( - O - N = O)}}\) as a part of its molecular structure....
Bond Linking Monomers in Polymers: Every living thing is made up of various proteins, enzymes, certain peptide hormones, carbohydrates, nucleic acids, polyphenolics etc. are important...
Higher animals possess an elaborated circulatory system that consists of a muscular and chambered heart, a network of blood vessels, and an extracellular fluid called...
Machines: Do you know we can easily lift heavy loads with a small effort? Do you know we can make the work easier with the...
Algebra of Complex Numbers: Complex numbers have wide applications in various fields of science, such as AC circuit analysis. Learning about the algebra of complex numbers...
The Lanthanoids: How many elements do you think there are in and around us? They can be counted, however counting them on your fingers is...
Important Trends and Anomalous Behaviour of Carbon: You know how important carbon is for our existence. Even our bodies are largely composed of carbon compounds....
Preparation of Colloidal Solutions: As we know, all solutions contain two entities in them, a solvent and a solute, mixed together to form a solution....
Deliquescence: We all must have seen tiny silica gel packets inside shoe boxes, new bags, and other gadgets, and they are there for a reason....
Periodic Trends in the Properties of Elements: The long form of the periodic table or the modern periodic table can also be called Bohr’s table...
Occurrence of Group 17 Elements: On the periodic table, the halogens are to the left of the noble gases. Fluorine \(\left( {\rm{F}} \right){\rm{,}}\) chlorine \(\left(...
Dinitrogen: Nitrogen is a colourless, odourless, and tasteless element that is plentiful in nature. Daniel Rutherford, a Scottish physician, was the first to discover it...
Drug-Target Interaction: As we've seen, chemistry plays a crucial role in practically every aspect of our lives. Medicinal chemistry is one such topic that is...
Biotechnology: The application of engineering science principles and technological methods on biological systems, like microorganisms, higher animals, and plants, intending to carry out chemical, environmental...
Health Organisations: Did you know that ischemic heart disease is the leading cause of disease worldwide? Last year heart disease killed \(4.77\) million people in...
Neural and Hormonal Control of Digestion: Taste and smell are related. What happens when we walk past a fast-food stall and catch a whiff of...
Unleash Your True Potential With Personalised Learning on EMBIBE
Create Free Account