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For simplicity in calculations it is often convenient to consider a surface perpendicular to the flux lines. If the electric field is uniform, the electric flux passing through a surface of vector area A is = = , where E is the electric field (having the unit V/m), E is its magnitude, A is the area of the surface, and θ is the angle between ...
No charge is enclosed by the sphere. Electric flux through its surface is zero. Gauss's law may be expressed as: [6] = where Φ E is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within V, and ε 0 is the electric constant.
A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, 'ideal' wire. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or magnetic field. [1]
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
= = , where is the net electric flux passing through the surface, is the charge enclosed in the Gaussian surface, is the electric field vector at a given point on the surface, and is a differential area vector on the Gaussian surface.
DC power transmission through a coaxial cable showing relative strength of electric and magnetic fields and resulting Poynting vector (=) at a radius r from the center of the coaxial cable. The broken magenta line shows the cumulative power transmission within radius r , half of which flows inside the geometric mean of R 1 and R 2 .
The current flowing through the resistance of the conductor also dissipates energy as heat in the material. Thus eddy currents are a cause of energy loss in alternating current (AC) inductors , transformers , electric motors and generators , and other AC machinery, requiring special construction such as laminated magnetic cores or ferrite cores ...
The flux through each patch is equal to the normal (perpendicular) component of the field, the dot product of F(x) with the unit normal vector n(x) (blue arrows) at the point x multiplied by the area dS. The sum of F · n, dS for each patch on the surface is the flux through the surface. Here are 3 definitions in increasing order of complexity.