lesson_4_-_Field_Potential_and_Gauss - EE3321...

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EE3321 ELECTROMAGNETIC FIELD THEORY Lecture 4 Highlights 1. Electric Potential The electrical potential difference is defined as the amount of work needed to move a unit electric charge from the second point to the first, or equivalently, the amount of work that a unit charge flowing from the first point to the second can perform. The potential difference between two points a and b is the line integral of the electric field E : The integration path is an arbitrary path connecting a point A of known potential to the observation point B as shown below Note: In this sketch ds = dl. The angle θ is the angular aperture between the E field and the length differential vector. Exercise 1 : Let E = E o z for z>0. Find φ E between a) A = (0, 0, 0) and B = (1, 1, 0) b) A = (0, 0, 0) and B = (1, 1, 1) When the E field has no curl, i.e. when the line integral does not depend on the specific path C chosen but only on its endpoints. The line integral cannot be used to compute the potential if which is the case of a nonconservative electric field caused by a changing magnetic field. Exercise 2: Show that E = E o z is conservative. When the magnetic field is constant in time, it is possible to express the electric field as the gradient of the electrostatic potential It also follows that the line integral of the electric field is path independent.
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Exercise 3 : Let V = V o z for z>0. Determine the electric field E . Consider for example the potential of a charged sphere with constant negative charge volume density. For reference, the potential is set to zero for a reference point at infinity. If a test charge approaches the charged sphere it will experience a decreasing potential as shown below. The potential is symmetric and decreases as the observation gets closer to the sphere. The concentric orbits in the figure represent lines of equal potential. Exercise 4:
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lesson_4_-_Field_Potential_and_Gauss - EE3321...

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