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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
What is the surface integral of electric field?
The surface integral of the electric field is the flux of the electric field through a closed surface. Mathematically, it is given by the surface integral of the dot product of the electric field vector and the outward normal vector to the surface. This integral relates to Gauss's law in electrostatics, where the total electric flux through a closed surface is proportional to the total charge enclosed by that surface.
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?
(a) On the surface of the balloon, the electric intensity is perpendicular to the surface and is constant. The electric potential varies across the surface with the highest value at the region of highest charge density. (b) Inside the balloon, the electric intensity and potential will be zero since the Gaussian surface does not enclose any charge. (c) Outside the balloon, the electric intensity decreases inversely with the square of the distance from the center of the balloon, while the electric potential also decreases with distance, following a similar inverse square law.
What did you mean by surface integral of electric field?
The surface integral of an electric field represents the total electric flux passing through a closed surface. It is a way to quantify how much an electric field penetrates a given surface area. Mathematically, it is calculated by integrating the dot product of the electric field and the differential area vector over the surface.
What do you mean by electric flux in electrostatics?
Electric flux is a measure of the number of electric field lines passing through a given area. It is defined as the dot product of the electric field and the surface area vector, and represents the flow of electric field through a surface. The electric flux is used to understand how electric fields interact with charged objects and surfaces.
What is meant by total normal electric induction over a surface?
Total normal electric induction over a surface refers to the total electric flux passing through the surface when the electric field is perpendicular to the surface. It is a measure of the total electric field passing through the surface and is calculated by the dot product of the electric field and the surface area vector.
A nonuniform electric field is directed along the x-axis. What is the net electrical flux passing the cylindrical surface?
The net electrical flux passing through a cylindrical surface in a nonuniform electric field is given by the integral of the electric field dot product with the surface area vector over the surface. The flux depends on the strength and direction of the electric field, as well as the shape and orientation of the surface.
Why is electric field inside a ring is zero?
The electric field inside a uniformly charged ring is zero because the field contributions from each infinitesimal charge element cancel each other out due to symmetry. The horizontal components of the electric fields from diametrically opposite charges cancel each other, while the vertical components add up to zero. Thus, the net electric field inside the ring is zero.
What is the name of a symbol of electric flux?
The symbol of electric flux is typically denoted by the Greek letter Φ (Phi). It is used to represent the total electric field passing through a given surface.
How do you derive the pi value using integral?
For example, by calculating the surface of a circle, using an integral.
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.
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.
