2. Four point-charges {q,-q, q,-9} are located on the z-axis at -20 + a/2 and -zo – a/2, respectively, as indicated in the (a) What is the exact total electrostatic potential energy U of this configuration of these four charges?

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2. Four point-charges {q,-q, q, -q} are located on the z-axis at positions 2o+a/2, zo-a/2,
-z0 + a/2 and -zo – a/2, respectively, as indicated in the figure.
(a) What is the exact total electrostatic potential energy
U of this configuration of these four charges?
Two Finite Dipoles
(b) For zo > a, use the expansion
1
1-r+- +... to find the leading
1+1
term of U in powers of a/zo (in addition to the 20-independent term -q/[2n€pa]).
(c) Assuming the charges +q at z = 20 + a/2 form a rigid dipole p, and the charges
+q at z = -20 +a/2 form a rigid dipole p2, are the two dipoles attracted to each
other or repelled from each other?
Transcribed Image Text:2. Four point-charges {q,-q, q, -q} are located on the z-axis at positions 2o+a/2, zo-a/2, -z0 + a/2 and -zo – a/2, respectively, as indicated in the figure. (a) What is the exact total electrostatic potential energy U of this configuration of these four charges? Two Finite Dipoles (b) For zo > a, use the expansion 1 1-r+- +... to find the leading 1+1 term of U in powers of a/zo (in addition to the 20-independent term -q/[2n€pa]). (c) Assuming the charges +q at z = 20 + a/2 form a rigid dipole p, and the charges +q at z = -20 +a/2 form a rigid dipole p2, are the two dipoles attracted to each other or repelled from each other?
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Step 1

Given, there are four electrostatic charges q,-q, q,-q at the position z0+a2, z0-a2,-z0+a2  ,- z0-a2 respectively

a. The total electrostatic potential of the system is 

U=-14πε0q2a+14πε0q22z0-14πε0q22z0-a-14πε0q22z0+a2-14πε0q22z0-14πε0q2aU=q24πε0-1a+12z0+12z0-a-12z0+a2-12z0+1a=q24πε012z0-a-12z0+a

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