Curriculum
Introduction to electric field:- When an electric charge ‘q₀’ is brought near to another charge ‘q’, then they experience a force which may be attractive or repulsive. This force on charge ‘q₀’ due to charge ‘q’ is confined in a certain region. So
“The region or space around the charge in which the electrostatic force of attraction or repulsion due to charge can be experienced by any other charge is known as electric field.”
Electric field Intensity:- The electric field intensity (or strength) at a point in an electric field is the force experienced by a unit positive charge (or a test charge q₀) placed at that point. Mathematically it is denoted by E. So electric field = force / unit +ve (test) charge
i.e
E^{\rightarrow}=F^{\rightarrow} / q_{-} 0
\vec{E}=\frac{\vec{F}}{q_0}
The electric field (E) is a vector quantity. Its direction is same as that of force .
In S.I. system, unit of is Newton/Coulomb (i.e N C⁻¹) & in C.G.S system unit of is dyne/stat coulomb.
Dimensional formula of electric field (E) →
; Also dimensional formula of q = [C]
Electric field Intensity due to a point charge:- let us consider two particles A & B separated by a distance ‘r’. (i.e A B = r). Let ‘+q’ be a point charge at point A. We have to calculate electric field intensity at point B. Imagine a small +ve test charge ‘q’ at point B.
when the charge is distributed on a volume of an object, then the distribution is called volume charge distribution & the charge distributed per unit volume is called volume charge distribution or density. It is denoted by P.
Mathematically,
For small volume element, volume charge density is given by
Expression for force :- Proceeding in the same way as in case of linear charge distribution, we have
The general expression for the total force on a test charge q₀ due to n-discrete point charges & all the three kinds of charge distributions is given by the relation.
Hence the proof
i.e aptrotute electrical fermitivity represent the electrical behaviour of physical quality. Permitivity E of a material is simply defined as the extend of difficulty with which the material allows the electric line of force to fast through it. in vaccum or air, it is least (i.e 8.85 , So it is knows as absolik fermitivity.
Proof :- Let us consider a point charge ‘q₁’ is placed at a point ‘A’ with position vector (r⃗₁). We have another point charge q₂, which is placed at infinity from point charge q₁. This point charge ‘q₂’ is to be brought to the position ‘B’ with position vector (r⃗₂). Here AB = r⃗₁₂.
Now, electric potential at ‘B’ due to charge q₁ at ‘A’ is
Also, we know that, work done in carrying a charge ‘q₂’ from ∞ to B is
Work = Potential × charge [ ∴ ]
i.e.
Putting the value of eq (1) in eq (2), we have
This work done is stored in the form of energy known as potential energy (W = U). Hence eq (3) may be re-written as
GAUSS’S APPLICATIONS
Area Vector :- Basically Area is a scalar quantity. It may be treated as vector. For this let us consider a small element of area ‘ds’ of a surface having surface area ‘S’.
The direction of ‘ds’ is taken perpendicular (normal) to the surface. If the direction is represented by a unit vector ( ) then the area vector is given by
Where dS = magnitude of the area element.
Electric flux :- Electric flux linked with any surface is defined as the total no. of electric lines of force that passes through the surface. It is denoted by φ.
Explanation :- Let a surface area ‘S’ be placed in uniform electric field . Take a small area element dS’ from the surface having surface area ‘S’. If θ is the angle between
If dS, then the electric flux of the field E over an area element dS’ is given by
Here the component of normal to area element is . Hence from (1), we can say that Electric flux (φ) is defined as the dot product of electric field & the surface area.
Now, the electric flux over the whole area of the surface is
Hence electric flux is also defined as the “surface integral of electric field over a surface (or closed surface)”.
+ve electric flux → when
Zero → when
–ve → when
By using the result:
The S.I unit of electric flux is N m²/C & the dimensional formula of electric flux is