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1800-102-2727Have you ever thought of how an electric field acts? Can we visualise these fields in any way ? Are these field lines just for visual need or do they have the importance to draw inferences from? Here we will walk through all these.
Electric flux can be understood by comparing the water flow through a passage. If we place a ring perpendicular to flow in the passage the water flowing through the ring area can be considered as flux. More is the water flow, more is the flux and stronger the current. If we put the ring parallel to the flow, no water will pass through the ring’s cross section. If we put the ring inclined to the flow, the water coming out from the ring is nothing but the water passing through the component of the ring area vector along the flow in the passage.
Table of contents:
Michael Faraday first developed the idea of visualising electric field lines. They are also known as electric lines of force. They are imaginary lines. For an electric charge q, the electric field at a distance r is given by,
$E=\frac{{F}_{e}}{{q}_{0}}=\left(\frac{kq{q}_{0}}{{r}^{2}}\right)\times \frac{1}{{q}_{0}}=\frac{kq}{{r}^{2}}$
Where $k=\frac{1}{4\pi {\epsilon}_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$
So, the direction of the electric field due to a charge at a point actually is the direction of force it would exert on a unit positive charge.
For a positive charge, the electric field lines will be radially outwards (as a bulb emits light). For a negative charge, the electric field lines will be radially inwards.
a. Electric lines of forces originate at a positive charge and terminate at a negative charge. If two charges are close to each other, the electric field lines will be as shown below.
b. For an isolated charge, the electric field lines terminate/originate at infinity ().
c. Tangent drawn at any point on the electric line of force gives the direction of the net electric field at that point. If we take tangents at various points along an electric field line, they depict the direction of the electric field at each of those points.
d. Electric field lines do not form a closed loop. The points of origination and termination of a line of force should be different. An electric field line originates from a positive charge and ends at a negative charge.
e. For a system of two charges having equal magnitude and opposite nature, electric field lines are always symmetric about the line joining the two charges.
f. Electric field lines are always perpendicular to the surface of the conducting charged body.
g. For a particular charge, the number of electric lines of force is an independent choice. It means that for a given magnitude of the charge, the electric lines of forces can vary.
The magnitude of the charge is directly proportional to the number of electric lines of
force originating or terminating at the charge. This choice is arbitrary but should be proportional for a given case. It means that if for a +q charge, we take four
lines, then for a +3q charge, the lines of forces should be triple, i.e., twelve.
h. Two electric field lines should never intersect. The electric field is a vector quantity and it cannot have two different directions at the same point.
i. The electric lines of force deviate from a positive charge and converge towards a negative charge.
j. In a uniform electric field, all the electric field lines are equally spaced and parallel to each other. It is because the intensity of the electric field at every point in the region is the same. In a non-uniform electric field, the electric field lines are not equally spaced, i.e., they are converging or diverging. It means that the intensity of the electric field at each point in the region is not the same.
Electric flux is the measure of the number of field lines crossing through a surface. In the figure let’s say there are N number of lines passing through a surface area S which is perpendicular to the electric field E. So, in that case the number of lines passing through unit area is NS.
$\frac{N}{S}\propto E\Rightarrow N\propto ES$
We can conclude that the quantity ES is the electric flux e through the surface S.
$\varphi \propto N\propto ES$
It is a scalar quantity. It has a unit Nm2C-1. When the surface under consideration is not perpendicular to the electric field lines, the flux can be obtained by ${\varphi}_{e}=\overrightarrow{E}.\overrightarrow{S}=EScos\theta $
e=E.dS
Here, is the angle between the direction of the surface (i.e., normal to the surface) and the electric field.
For a positive charge, the electric field lines emerge from the charge. As we go far from the charge, the electric field decreases. This can also be seen from the image.
Q. In an electric field, the flux(ϕ) through a unit area decreases with the radial distance r as $\varphi \propto \frac{{\varphi}_{0}}{{r}^{2}}$. Comment on the charge particle if any in space.
A. We know that, flux is proportional to ES. Where E is the electric field and S is the area under consideration for that flux.
As is the flux through a unit area, ϕ∝E
It is given in the question that, $\varphi \propto \frac{{\varphi}_{0}}{{r}^{2}}\Rightarrow E\propto \frac{1}{{r}^{2}}$
So, there should be a charge at the origin.
Q. Calculate the flux through an area, 2m2 i+3m2 j for an electric field $\overrightarrow{E}=\left(3\hat{i}-2\hat{j}\right)N{C}^{-1}$
A. The flux coming out through an area can be calculated as,
Q. While drawing field lines emerging out from a point charge of +3 C, a student draws 9 lines. For a -9 C, how many field lines should he draw?
A. The number of field lines in a particular case should be proportional to the amount of charge. So 9×93=27 lines must be drawn and they should sink into the point charge.
Q. There is an electric field E=E1i. What is the flux through an imaginary area parallel to x-y plane?
A. Flux through an imaginary area can be calculated as, e=E.dS
Here, the area vector for a plane parallel to x-y plane is towards the k direction.
So, i.e., the flux is zero.
Q. Can electric field lines make a closed loop?
A. Electric field line is an imaginary line that depicts the direction of an electric field at a point in the region under consideration. An electric field line always originates from a positive charge and ends at a negative charge. Electric field lines cannot form a closed loop. The point of origin and termination of an electric field line of force should be different. A point can’t be both positive and negative at the same time. Let’s say an electric field line starts at point A and after passing through points B, C, D it ends on A. In that case it will imply that point A is a positive charge when the field line emerges out and it is a negative charge at the time when the field line ends into it. This is not possible as A is a point. If it were an object, it could have been a possible case when the body has positive and negative ends.
Q. Can an electric field line intersect another field line?
A. Two electric field lines should not intersect. The tangent at any point on an electric field line depicts the direction of the electric field. The electric field is a vector quantity and it cannot have two different directions at the same point (i.e., the point of intersection).
Q. How to recognise the presence of charge particles by inspecting the electric field lines?
A. Electric field lines are equally spaced and parallel to each other in a uniform electric field. This happens because the intensity of the electric field at every point in the region is the same. In a non-uniform electric field, the electric field lines are not equally spaced. Either they are converging or diverging. It means that the intensity of the electric field at each point in the region is not the same. In case, there is a presence of a positive charged particle, the electric field will diverge. And in case there is a presence of a negatively charged particle, the field lines will converge. Thus, we can detect any charged particle in that region.
Q. An electric field line is as shown in the figure. Comment on the feasibility of the scenario.
A. Electric field lines only emerge from a positively charged particle and end at a negatively charged particle. So it can never happen.