Electrostatics 2 Question 25
26. Eight point charges are placed at the corners of a cube of edge $a$ as shown in figure. Find the work done in disassembling this system of charges.
$(2003,2 M)$
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Solution:
- For potential energy of the system of charges, total number of charge pairs will be ${ }^{8} C _2$ or 28 of these 28 pairs 12 unlike charges are at a separation $a, 12$ like charges are at separation $\sqrt{2} a$ and 4 unlike charges are at separation $\sqrt{3} a$. Therefore, the potential energy of the system is given as
$$ \begin{aligned} U & =\frac{1}{4 \pi \varepsilon _0} \frac{(12)(q)(-q)}{a}+\frac{(12)(q)(q)}{\sqrt{2} a}+\frac{(4)(q)(-q)}{\sqrt{3} a} \\ & =-5.824 \frac{1}{4 \pi \varepsilon _0} \cdot \frac{q^{2}}{a} \end{aligned} $$
The binding energy of this system is therefore,
$$ |U|=5.824 \frac{1}{4 \pi \varepsilon _0} \frac{q^{2}}{a} . $$
So, work done by external forces in disassembling, this system of charges is $W=5.824 \frac{1}{4 \pi \varepsilon _0} \cdot \frac{q^{2}}{a}$
