How to Calculate Electric Field Strength
Gauss's law and Coulomb's law are two alternative ways of obtaining the electric field strength from a distribution of charge. An electric field is generated from and exerts forces on charged particles. The electric field is a vector field that is directed away from positive charge toward the negative. In Coulombs law, the magnitude of the electric field E at a point in space is proportional to the charge q over the distance s, from the source, squared: E = k*|q|/s^2, where k = 8.988e9 Nm^2/C^2. Gauss's law states that the total electric flux out of any closed imaginary surface is proportional to the total electric charge inside the surface: E*A = |q|/8.854e-12, where A is an imaginary surface area enclosing the charge.
Instructions
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Identify the charge source. For example, you may want to calculate the electric field at one micrometer in radius away from an electron. In this case the charge is |q| = 1.6e-19 C.
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Determine the radial distance for Coulombs law or the surface area for Gauss's law. The appropriate surface to use for this example is a sphere. The surface area of this shape is 12.56*r^2, where r is the radius of the spherical shell. For the current example r = s = 1 micrometer.
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Calculate the electric field. Both laws result in the same formula for the electric field E = 8.987e9*|q|/s^2= 1,437.9 N/C.
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Tips & Warnings
Gauss's law is better suited for obtaining the electric field for many symmetrical charge distributions, such as the field of a line of charge, an infinite plane sheet of charge, and the field between two oppositely charged parallel conducting plates.
References
Resources
- Photo Credit charge image by Dave from Fotolia.com
