You are integrating two vector quantities. The dot is there to indicate the scalar product of the electric field E and the infinitesimal bit of surface area dA.Jatin Kaushal said:This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there?
Thank you for your help
The scalar product that SteamKing mentions is also called the "dot product."SteamKing said:You are integrating two vector quantities. The dot is there to indicate the scalar product of the electric field E and the infinitesimal bit of surface area dA.
The dot multiplication symbol, also known as the "dot product" or "scalar product", is used in integration to represent the multiplication of two functions. This is commonly seen in the notation for a Riemann integral, where the integrand is written as the product of two functions.
The dot multiplication symbol is used in integration because it represents a specific type of multiplication, where the result is a scalar (a single number) rather than a vector. This is important in integration, as the result of an integral is a single value, rather than a function.
The dot multiplication symbol is different from the traditional multiplication symbol in that it represents a different type of multiplication. The traditional symbol represents the multiplication of two numbers or variables, while the dot multiplication symbol represents the multiplication of two functions.
Yes, the dot multiplication symbol can be used in other mathematical operations, such as finding the angle between two vectors or calculating the work done by a force on an object. It is a versatile mathematical tool that has various applications in different fields of science and engineering.
The dot multiplication symbol is necessary in integration as it represents a specific type of multiplication that is crucial in calculating integrals. While it can be replaced with the traditional multiplication symbol in some cases, it is not recommended as it may lead to confusion and errors in more complex integrals.