L18_a - CHARGE DENSITY(Important concept • Usually need...

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CONTINUOUS CHARGE DISTRIBUTIONS: CHARGED OBJECTS WITH FINITE SIZE Strategy: Break distribution into small charge elements Find contribution to electric potential or electric field from a given element Sum/integrate to find total V or E r ELECTRICAL POTENTIAL FROM A CONTINUOUS CHARGE DISTRIBUTION contribution to electric potential at P from charge element i q is: i i i r q k V = e for total V at P, sum over elements, take limit integral = = charge all over e e 0 lim r dq k r q k V i i i q i Identify r dq k dV e = as the contribution to V from the charge element dq
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EXAMPLE: Consider a uniformly charged ring of radius a and total charge Q . (a) At a point P a distance x from the centre of the ring along a perpendicular line through the centre of the ring, find dV , the contribution to V from a charge element dq . (b) Sum(integrate) over the whole charge distribution to find V at the point P. (c) Use the result from (b) to calculate the electric field at P.
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Unformatted text preview: CHARGE DENSITY (Important concept) • Usually need to convert sum/integral over charge elements into a sum/integral over spatial variables (i.e. x, y, z ) • Use concept of charge density o Linear charge density: for a uniformly charged line of length L and total charge Q , the linear charge density is L Q = λ o Surface charge density: for a uniformly charged plane of area A and total charge Q , the surface charge density is A Q = σ o Volume charge density: for a uniformly charged space of volume V and total charge Q , the volume charge density is V Q = ρ Example: Consider a uniformly rod of length L and total charge Q . Find the electric potential at a distance a along the rod axis from one end. Example: Consider a uniformly rod of length L and total charge Q . Find the electric potential at a distance a from one end along a line perpendicular to the rod....
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This note was uploaded on 03/08/2012 for the course PHYSICS 1051 taught by Professor Michaelmorrow during the Winter '12 term at Memorial University.

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L18_a - CHARGE DENSITY(Important concept • Usually need...

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