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Electric flux.

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Q: What represent the surface integral of electric field intensity?
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How do you derive the pi value using integral?

For example, by calculating the surface of a circle, using an integral.


What is the difference between definite integral and line integral?

Both kinds of integrals are essentially calculations of areas under curves. In a definite integral the surface whose area is to be calculated is planar. In a line integral the surface whose area to be calculated might occupy two or more dimensions. You might be interested in the animated diagrams in the wikipedia article for the line integral.


What are Line integral Surface integral and Volume integral in simple words?

A line integral is a simple integral. they look like: integral x=a to b of (f(x)). A surface integral is an integral of two variables. they look like: integral x=a to b, y=c to d of (f(x,y)). or integral x=a to b of (integral y=c to d of (f(x,y))). The second form is the nested form. A pair of line integrals, one inside the other. This is the easiest way to understand surface integrals, and, normally, solve surface integrals. A volume integral is an integral of three variables. they look like: integral x=a to b, y=c to d, z=e to f of (f(x,y,z)). or integral x=a to b of (integral y=c to d of (integral z=e to f of f(x,y,z))). the above statement is wrong, the person who wrote this stated the first 2 types of integrals as regular, simple, scalar integrals, when line and surface integrals are actually a form of vector calculus. in the previous answer, it is stated that the integrand is just some funtion of x when it is actually usually a vector field and instead of evaluating the integral from some x a to b, you will actually be evaluating the integral along a curve that you will parametrize to get the upper and lower bounds of the integral. as you can see, these are a lot more complicated. looking at your question tho, i dont think you want the whole expanation on how to solve these problems, but more so what they are and what they are used for, because these can be a pain to solve and there are also several ways to solve them indirectly. line integrals have an important part in physics because they alow us to calculate things such as work that have vector values rather than just scalar values as you can use these integrals to describe a particles path along a curve in a force field. surface integrals help us calculate things like flux, or how fluid flows over a surface. if you want to learn more, look into things like greens theorem, or the divergence theorem. p.s. his definition of a surface integral is acutally how you find the volume of a region


What is the derivation of Coulomb's constant?

Coulomb's constant 'k' in the equation F=kQQ/r2 is derived from Gauss's law. Gauss's law stated that the charge enclosed by a theoretical surface is equal to the permittivity constant, represented by the Greek letter epsilon (because I can't use an epsilon, I will use an X) times the electric flux through the surface. Flux is equal to the closed integral of electric field vector dot the vector dA (infinitesimal change in surface area) of the surface. Becasue the surface surrounding one point charge is a perfect sphere, the dot product can be ignored (The surface is uniform and every change in area is normal to the electric field), and the Electric field is constant so it can be brought out of the integral leaving integral dA. When the integral is solved, the resulting equation is XEA=Q. A equals the surface area of the sphere so XE(4*pi*r2)=Q and E=Q/(4*pi*X*r2) and because F=EQ, F=QQ/(4*pi*X*r2). This is probably looking pretty familiar. All we have to do is make k=1/(4*pi*X) to make this equation equal to good old Coulomb's law. X, the permittivity constant equals 8.854*10-12 Farads per meter, or coulombs squared seconds squared per kilograms meters cubed. If you substitute this constant into the equation k=1/(4*pi*X), you obtain Coulmb's constant.


What structure does surface area represent in a cell?

plasma member

Related questions

Electric charge is uniformly distributed on the surface of a spherical balloon. Show how electric intensity and electric potential vary (a) on the surface (b) inside and (c) outside?

Tes


What do you mean by electric flux in electrostatics?

Under an electric field, magnitude and direction of electric intensity is different in every point.If the electric intensity can be defined through a closed line (direction of electric intensity will be along the tangent of any point of that line)this is called electric lines of force. Electric lines of forces passing through an closed electric surface perpendicularly, is called electric flux.


What did you mean by surface integral of electric field?

It means that a surface is divided into many small pieces, the area of each piece is multiplied by a quantity (for example, the electric field - possibly a vector multiplication), and everything is added up in the end.


Why is electric field inside a ring is zero?

If you refer to Gauss's law, it states the electric flux through any closed surface is proportionate to the enclosed electric charge. The electric flux density is the same as the electric field intensity. A Gaussian surface is a closed, three dimensional surface (there's no holes in it). Here's an example to help clarify what this is and is not saying. Suppose I have a clear glass ball. The "light charge" inside the ball is zero because there is no light source inside the ball. If I put the ball in the sunlight, light will go into one side, and out the other (ignore any sort of prism effect, etc. just don't think too hard about this example!). This ball still does not have an internal "light charge" because the light flowing into the ball is equivalent to the light flowing out (the "light density" through the surface sums to zero, or the line integral of the light density = 0 for this surface). If I put a light source inside the ball, the line integral of "light density" leaving the ball would be proportional to the "light charge" inside the ball; in other words the line integral tells you what is enclosed by the Gaussian surface (my fictitious light source, but not the sun). Even if I put it in the sunlight again, the line integral will remove the "light charge" due to the sun and I will be left with only my internal light source. In both these instances, absolutely nothing is being stated about the "light density" / "light intensity" inside the ball. For both instances, there is a light intensity INSIDE the ball, even though the "light charge" inside is non zero in only one case. Relating to the question, this means if you have a Gaussian surface (such as a sphere), and it has/does not have an enclosed electric charge, you can have an electric field through the sphere - the fact this field is there tells you nothing about the internal charge of the Gaussian surface until you perform the line integral to measure what's coming in and what's going out. So, what I'm stating is the question is not true - the electric field is not necessarily zero inside a Gaussian surface, even if the surface does not contain an electrically charged particle. This should be easily seen by taking the typical point charge example: You have a point charge, and you draw the Gaussian surface around it. The point charge radiates electric field lines in all directions away from itself. If you move the Gaussian surface to the left until the point charge is no longer enclosed in it, you will see the radiating electric field lines due to this point charge still go into and out of the surface (so there is an electric field due to the point charge inside the surface), but the point charge is no longer enclosed by the surface (so the line integral sums to zero).


What is meant by total normal electric induction over a surface?

It is the actually the electric flux i.e. integral Eds where E is electric field and ds is elemental area. It can be also defined as the no. of lines of force passing through a given area.


How do you derive the pi value using integral?

For example, by calculating the surface of a circle, using an integral.


What is the definition for intensity of insolation?

Intensity of insolation refers to the intensity of the sun's rays on the earth's surface. It is a measure of solar energy that is received by a given surface area at a given time.


Why 400kVA and above the transmission line have bundled conductor?

To reduce the electric field intensity at the surface of the conductor which can lead to corona discharge and insulation breakdown. By using bundled conductors, the electric field is distributed between the four (in the case of 400-kV lines) conductors, thus reducing the field intensity per conductor.


What is the difference between definite integral and line integral?

Both kinds of integrals are essentially calculations of areas under curves. In a definite integral the surface whose area is to be calculated is planar. In a line integral the surface whose area to be calculated might occupy two or more dimensions. You might be interested in the animated diagrams in the wikipedia article for the line integral.


Why surface of electric machine are made smooth?

The surface of electric machine are smooth why


What is maximum and minimum electric flux?

As we know that electric flux is the total number of electric lines of forces passing through a surface. Maximum Flux: Electric flux through a surface will be maximum when electric lines of forces are perpendicular to the surface. Minimum flux: Electric flux through a surface will be minimum or zero when electric lines of forces are parallel to the surface.


What protein that projects from the outer surface of the membrane is termed?

integral protein