O Rutgers, The State University of New Jersey. Department of Physics&AstronormyExample: Find the electric field and the potentialat the center of a thin square conductor of side Land total charge Q.Ecenter 0,Vcenter 0L/28k11xp:dx2.center=2+r22O Rutgers, The State University of New Jersey. Department of Physics & Astranomy

Question
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I do not understand how the professor came to the conclusion for the Vcenter equation.

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Step 1

The potential at the center of the square would be given by the sum of individual potentials at the center due to conductor segments of length L/2. Consider the diagram below of one such segment.

Step 2

Step 3

The potential due an length element dx of the conductor at the center is given as,

Here, dq is the charge in dx length, k is the Coulomb’s constant and r is the line element’s distance from the center.

Integrate above equation to obtain the potential at the cen...

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