Potential along the X Axis due to Charge Distribution?

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SUMMARY

The discussion centers on the electric potential generated by a uniformly charged square in the yz-plane, specifically analyzing the potential along the x-axis. The textbook indicates that the potential graph exhibits a bell curve with a maximum at x=0, which contrasts with the point charge potential equation v = k|Q|/(x) that suggests infinite potential as x approaches zero. The resolution lies in recognizing that the potential due to a uniformly charged square requires integrating contributions from all sides, leading to a finite maximum rather than infinite potential at the center.

PREREQUISITES
  • Understanding of electric potential and its mathematical representation.
  • Familiarity with the concept of charge distribution, particularly uniform charge distribution.
  • Knowledge of the potential due to line charges and integration techniques.
  • Basic grasp of scalar quantities in physics.
NEXT STEPS
  • Study the derivation of electric potential from continuous charge distributions.
  • Learn about the integration of electric fields from multiple charge sources.
  • Explore the concept of electric potential in three-dimensional charge distributions.
  • Investigate the differences between point charge potential and potential from extended charge distributions.
USEFUL FOR

Physics students, electrical engineers, and educators seeking to deepen their understanding of electric potential and charge distributions.

Joseph Nechleba
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I have a question regarding electric potential and infinity. So,

"A square of side length a with uniformly distributed positive charge lies on the yz plane with its center at the origin. What does the graph of the potential along the x-axis look like?

The answer given in the textbook is a bell-curved-shaped graph with its maximum at x=0. My question is, Why is there a maximum? According to the equation for potential of a point charge, v = k|Q|/(x), shouldn't the potential approach positive infinity as x approaches zero from either direction, as electric potential is a scalar and the charge is uniform?

I am hoping someone can clear my conceptual misunderstanding.
 
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Potential for a point charge is kq/x but the same expression is not true for a charged square. Take a point at a distance x from centre of square along x axis. Now find the potential at that point due to 4 sides of the square. You must know the expression for potential at a point due to a line charge. That times 4 will give total potential because potential is scalar.
 
That makes perfect sense! Thank you for your prompt response!
 

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