The integral of the electric field, E, dotted with the differential path length, dl, around any closed loop will be zero when the loop encloses no net electric charge.
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.
The formula for calculating the electric flux () through a closed surface is EdA, where E is the electric field and dA is a differential area element on the surface.
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.
To evaluate the integral in Gauss's law, you need to calculate the electric flux through a closed surface. This involves finding the dot product of the electric field and the surface area vector at each point on the surface, and then integrating over the entire surface. The result of this integral will give you the total electric flux through the surface, which is related to the total charge enclosed by the surface.
The curl of an electric field is zero because electric fields are conservative, meaning the work done by the field on a charge moving around a closed path is zero. This implies that the circulation of the electric field around any closed loop is zero, leading to a curl of zero.
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.
The formula for calculating the electric flux () through a closed surface is EdA, where E is the electric field and dA is a differential area element on the surface.
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.
To evaluate the integral in Gauss's law, you need to calculate the electric flux through a closed surface. This involves finding the dot product of the electric field and the surface area vector at each point on the surface, and then integrating over the entire surface. The result of this integral will give you the total electric flux through the surface, which is related to the total charge enclosed by the surface.
Maxwells equations are a set of 4 equations that explain the fundamentals of Electricity and Magnetism. They read like this. 1. The Closed integral of Electric Field with Respect to Area is equal to Enclosed Charge over epsilon not. 2. The Closed integral of Magnetic field is equal to zero. 3. The Closed integral of Electric Field with repsect to distance is equal to the negative derivitive of magnetic flux with respect to time. 4. The Closed integral of Magnetic Field with respect to distance is equal to the quantity of mu not times enclosed current plus the quantity of epsilon not mu not times the derivitive of Electric Flux with respect to time. In order to really understand the applications of these equations, I would suggest taking an entire calculus based physics course on Electricity and Magnetism, as well as a Calculus Course.
which electric element should be used so as to open the closed electric circuit
A closed circuit.
yes it does have to be a closed circuit
Electric Current
The curl of an electric field is zero because electric fields are conservative, meaning the work done by the field on a charge moving around a closed path is zero. This implies that the circulation of the electric field around any closed loop is zero, leading to a curl of zero.
An electric current will flow if there is a voltage, and a conducting path (usually a closed circuit is required).An electric current will flow if there is a voltage, and a conducting path (usually a closed circuit is required).An electric current will flow if there is a voltage, and a conducting path (usually a closed circuit is required).An electric current will flow if there is a voltage, and a conducting path (usually a closed circuit is required).
When a circuit is closed, meaning there is a complete path for the electric current to flow, the current will flow from the positive terminal of the voltage source through the circuit components and back to the negative terminal. This flow of current allows electrical energy to be transferred and work to be done in the circuit.