Surface Charge Density Formulas & Examples
Surface Charge Density is the amount of charge per unit of a two-dimensional surface area. It is a measure of how much quantity of electric charge is accumulated over a surface. It is expressed by the symbol σ and the unit in the SI system is Coulombs per square meter i.e Cm–2.
If q is the charge and A is the area of the surface, then the Surface Charge Density is given by; σ=qA,
In electromagnetism, it is expressed as the quantity of electric charge per unit volume of one, two, or even three-dimensional space.
The topic covers many numerical problems of charge and magnetism even.
Importance of Surface Charge Density in Physics
The topic of Surface Charge Density is quite important in the Physics of higher classes. They have a considerable good weightage in Physics of JEE and other competitive exams. Electric charge and electricity have always been a choice topic for question setters. Not only this if the concept of this topic is clear then many numerical problems of this kind and also those related to magnetism will be easily solved and that will bring good marks.
Study with Vedantu
Vedantu has prepared many sample papers and good study material on this topic to make the concept easy for the students. The subject experts in Vedantu know well with their years’ experience how and which topic needs to be more focussed for the students. Keeping the benefits of the students in their minds, they have provided relevant question answers on this topic. The students can bring clarity in their concept and get enough confidence for any kind of numerical problem based on this topic.
Example 1
1. A large plane sheet has an area of 50 cm2 and has a charge of 3mC uniformly distributed over it. Find the Surface Charge Density.
Solution:
q = 3 mC = 3 × 10–3 C, A = 50 cm2 = 5 ×10–3 m2, σ = ?
σ=qA=(3×10−3)(5×10−3) = 0.6Cm−2
2. A cuboidal box penetrates a huge plane sheet of charge with uniform Surface Charge Density 2.5×10–2 Cm–2 such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box.
Solution:
Charge enclosed by the box = charge on the portion of the sheet enclosed by the box.
The area of the sheet enclosed; A = area of the smallest surface of the box
= 5 cm × 3 cm = 15 cm2 = 15 × 10–4 m2
Charge density; σ= 2.5 ×10–2 Cm–2
Charge enclosed; q = σA = (2.5×10−2)(15×10−4) = 37.5×10−6C = 37.5µC
Practice question:
The same charge is given to four thin plane laminas of different shapes; an equilateral triangle, a square, a regular hexagon, and a circular one. All of these have the same perimeter. Then the lamina with the maximum Surface Charge Density has the shape as that of :
an equilateral triangle
a square
a regular hexagon
a circle
Ans (a)
FAQs on Surface Charge Density Formula
1. How many types of charge densities are there?
Charge density is the quantity of charge in a particular space. The space may be one dimensional, two dimensional, or even three dimensional, and based on this there are three types of charge densities. There are three types of charge densities depending upon the surface which may be one, two, or three-dimensional.
Linear charge density: Charge per unit length. Where the quantity q of charge is spread over length m. It is expressed in Coulomb per meter in the SI system
Surface Charge Density: Charge per unit surface area. Where the quantity q of charge is spread over an area of the square meter. It is expressed in Coulomb per square meter in the SI system.
Volume charge density: Charge per unit volume. Where the quantity q of charge is spread over a volume of cubic meters. It is expressed in Coulomb per meter cube in Si units.
However, the most important that we regularly deal with is Surface Charge Density.
2. What is the importance of Surface Charge Density?
It is very important to determine the charge in an electric field. This concept of Surface Charge Density has many applications both in Physics and chemistry. It is used in electrokinetic phenomena like electrophoresis, electro-osmosis, and sedimentation potential. In chemistry, it is of great importance in nanoparticles and even drug delivery. Surface Charge Density determines the amount of interaction that the nanoparticles will have with the biological components of the body and thus the drug from nanoparticles can be prepared accordingly.
3. A metallic plane sheet of area 20 cm2 has a charge of 3mC uniformly distributed over it. Calculate the Surface Charge Density.
In the given problem the units of charge and area are in mC and centimeter, so first, they need to be converted into SI units and then proceed according to the formula of Surface Charge Density.
Charge q is given 3 mC
So,
In SI unit q= 3 × 10–3 C,
Given Area, A = 20 cm2
In the SI unit here A= 2 ×10–6 m2,
The Surface Charge Density σ=qA
Therefore,
Here q= (3×10−3) x (2 ×10–6) =6 x 10-9.
4. A cuboidal box penetrates a huge plane sheet of charge with uniform Surface Charge Density 2.5×10–2 Cm–2 such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box.
Charge enclosed by the box = charge on the portion of the sheet enclosed by the box.
The area of the sheet enclosed; A = area of the smallest surface of the box
= 5 cm × 3 cm = 15 cm2 = 15 × 10–4 m2
Charge density; σ= 2.5 ×10–2 Cm–2
Charge enclosed; q=σA=2.5×10−2×15×10−4=37.5×10−6C=37.5μC
5. What is the weightage of the topic Surface Charge Density in JEE Physics?
The topic of Surface Charge Density holds good weightage in JEE mains and other competitive exams. Its apparent weightage in the exam paper is 18% but many other topics related to or based on this concept can increase its total weightage in the question paper. The vastness of this topic even includes many topics of chemistry as well. The numerical problems from this topic are not that hard to attempt. The topic can be an easy scoring one if the concept is clear. Students need to have good practice of this chapter and revise it regularly. This can be easily achieved through study materials from Vedantu.
