Eight charges,each of magnitude q,are placed | vedclass

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(D) The length of the body diagonal of a cube with side $a$ is $\sqrt{3} a$. The distance $r$ of each vertex from the centre $O$ of the cube is half o

Vedclass · Accepted Answer

$\frac{4 q}{\sqrt{3} \pi \varepsilon_0 a}$

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(D) The length of the body diagonal of a cube with side $a$ is $\sqrt{3} a$. The distance $r$ of each vertex from the centre $O$ of the cube is half of the body diagonal: $r = \frac{\sqrt{3} a}{2}$.Since there are $8$ identical charges $q$ at the vertices,the total electric potential $V$ at the centre $O$ is the sum of the potentials due to each individual charge:$V = 8 	imes \frac{1}{4 \pi \varepsilon_0} 	imes \frac{q}{r}$Substituting the value of $r$:$V = 8 	imes \frac{1}{4 \pi \varepsilon_0} 	imes \frac{q}{\frac{\sqrt{3} a}{2}}$$V = 8 	imes \frac{1}{4 \pi \varepsilon_0} 	imes \frac{2q}{\sqrt{3} a}$$V = \frac{4 q}{\sqrt{3} \pi \varepsilon_0 a}$

Eight charges,each of magnitude $q$,are placed at the vertices of a cube placed in a vacuum. The electric potential at the centre of the cube due to this system of charges is . . . . . . . ($\varepsilon_0 = $ permittivity of vacuum,$a = $ length of each side of the cube.)

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