Show that the work required to assemble four identical point
charges of magnitude q on the corners of a square of side a is
To calculate the work to assemble any number of point charges
you can proceed as follows: - Numerate each charge. - Assume
charges are brought from an infinite distance. - Charge 1 is
brought first and placed on corner 1. This charge does not
requires any work because there is no electric field present. -
Charge 2 is brought then and placed on corner 2, charge 3 is
brought and placed on corner 3 and so on. Charge 2 requires a
work keq2/a. Charge 3 requires a work keq2/a + keq2/(a21/2)
(work due to charges 1 and 2 already present). Charge 4 requires
a work keq2/a + keq2/(a21/2) + keq2a (work due to charges 1, 2
and 3 already present). The work needed to get the desired
configuration is obtained adding each required work: keq2/a +
keq2/a + keq2/(a21/2) + keq2/a + keq2/(a21/2) + keq2/a. =
(keq2/a)(1 + 1 + 2-1/2 + 1 + 2-1/2 + 1) = 5.41 keq2/a. The axis
x is the axis of symmetry of a ring uni