PPE15_UniformChgDist

# PPE15_UniformChgDist - Potential Uniform Charge...

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Potential Potential Uniform Charge Uniform Charge Distributions Distributions © RHJansen

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Example 1 A conducting hoop with charge Q and radius R . © RHJansen a. Determine the electric field at the hoop’s center. We need no math for this one. Each charge around the hoop creates a field at the center that points away from the charge. Since the charges are evenly distributed on a round conductor, the field from the charge on any part of the hoop is always canceled by a charge on the opposite side of the hoop. E = 0
Picture the hoop divided into small sections, each containing a small amount of charge q a distance r from the center. An individual section can be solved using: However, there are a lot of these sections, and they are very small. Add them up. Example 1 A conducting hoop with charge Q and radius R . © RHJansen b. Determine the electric potential at the hoop’s center. q r V = κ θ ρ V = κΣ ι V = κ 1 + 2 + 3 + ... V = κ Θ Ρ They add up to the total charge Q and r = R .

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Example 2 © RHJansen a. Determine the electric field at point P in terms of R , x , & Q . Use the formula: Divide the hoop into elements of charge dQ . Each element of charge creates an element of the electric field dE . A point P is located a distance x to the right of the center of a hoop with a charge of Q and radius R . E = κ Θ ρ 2 dE = κ δΘ 2 x R P dE r dQ θ dE points away from positive dQ . Had dQ been negative, all formulas and values that follow would be the same. The only difference would be the direction of field vectors.
Example 2 © RHJansen For every dQ there is another dQ on the opposite side of the hoop. It also creates a field dE . The field vectors are not on an axis. Go to components. A point P is located a distance x to the right of the center of a hoop with a charge of Q and radius R . dE x θ R P dE r dQ dE = κ δΘ ρ 2

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Example 2 © RHJansen The dQ ’s are equal.
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## This note was uploaded on 07/21/2009 for the course PHYSICS 7B taught by Professor Packard during the Spring '08 term at Berkeley.

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PPE15_UniformChgDist - Potential Uniform Charge...

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