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Exercise:
Show that the potential difference between two pos A and B in the field of a uniformly charged plate with surface charge density sigma is given by Delta V fracsigma varepsilon_ left r_A - r_B right where r_A and r_B are the distance of po A and B from the plate respectively.

Solution:
We ase that A and B are on the same electric field line. The uniform electric field of a charged plate surface charge density sigma is E fracsigmavarepsilon_ The work done by the electric field on a test charge q moving from A to B is thus W_Ato B F d F left r_B - r_A right q fracsigma varepsilon_ left r_B - r_A right It follows for the potential difference Delta V_AB -fracW_Ato Bq -fracq fracsigma varepsilon_ left r_B - r_A rightq fracsigma varepsilon_ left r_A - r_B right
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Exercise:
Show that the potential difference between two pos A and B in the field of a uniformly charged plate with surface charge density sigma is given by Delta V fracsigma varepsilon_ left r_A - r_B right where r_A and r_B are the distance of po A and B from the plate respectively.

Solution:
We ase that A and B are on the same electric field line. The uniform electric field of a charged plate surface charge density sigma is E fracsigmavarepsilon_ The work done by the electric field on a test charge q moving from A to B is thus W_Ato B F d F left r_B - r_A right q fracsigma varepsilon_ left r_B - r_A right It follows for the potential difference Delta V_AB -fracW_Ato Bq -fracq fracsigma varepsilon_ left r_B - r_A rightq fracsigma varepsilon_ left r_A - r_B right
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Electrostatics
Tags
integral, plate, potential difference
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(3, default)
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0 (default)
Language
ENG (English)
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