Not really sure what it would be in rectangular coordinates...jtbell said:In principle, one can use any coordinate system for this problem. However, it's simpler to use spherical coordinates in this case. To see why, write ##\vec E## and ##\vec {dl}## in rectangular (Cartesian) coordinates.
emhelp100 said:Homework Statement
A point charge +Q exists at the origin. Find [itex]\oint[/itex] [itex]\vec{E} [/itex] [itex]\cdot \vec{dl}[/itex] around a circle of radius a centered around the origin.
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Why are cylindrical coordinates being used here?
Cylindrical coordinates are a type of coordinate system used to describe positions in three-dimensional space. They consist of a radius, an angle, and a height, and are often used in problems involving cylindrical or circular shapes.
Cylindrical coordinates use different variables to describe position compared to Cartesian coordinates. In cylindrical coordinates, the variables are radius, angle, and height, while in Cartesian coordinates, the variables are x, y, and z. Additionally, cylindrical coordinates are more suited for describing cylindrical or circular shapes, while Cartesian coordinates are better for rectangular shapes.
In electromagnetism, E.dl (electric field dotted with a differential length) is used to calculate the work done by an electric field on a charged particle. In cylindrical coordinates, the electric field is often not constant, so it is important to show that E.dl is 0 in order to accurately calculate the work done and understand the behavior of the electric field.
E.dl is calculated by taking the dot product of the electric field vector and the differential length vector. In cylindrical coordinates, the electric field vector is expressed as (Er, Eθ, Ez), and the differential length vector is expressed as (dr, rdθ, dz). The dot product of these two vectors is then integrated over the desired path to find the total work done by the electric field.
Yes, other coordinate systems such as spherical coordinates or even Cartesian coordinates can be used to show that E.dl is 0. The specific choice of coordinate system depends on the problem at hand and which system will make the calculations and analysis easier.