Five positive charges, each having charge q, | vedclass

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(A) $1$. Electric potential $(V)$ is a scalar quantity. The potential at the center $O$ due to a single charge $q$ at a distance $r$ is $V_i = \frac{1

Vedclass · Accepted Answer

$V=\frac{5 q}{4 \pi \varepsilon_0 r}$ and $\vec{E}=0$

Vedclass · Answer

(A) $1$. Electric potential $(V)$ is a scalar quantity. The potential at the center $O$ due to a single charge $q$ at a distance $r$ is $V_i = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$. Since there are five such charges, the total potential is the algebraic sum: $V = 5 	imes \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} = \frac{5 q}{4 \pi \varepsilon_0 r}$.$2$. Electric field $(\vec{E})$ is a vector quantity. For a regular polygon with identical charges at all vertices, the electric field vectors due to individual charges cancel each other out due to symmetry. Therefore, the net electric field at the center $O$ is $\vec{E} = 0$.

Five positive charges, each having charge $q$, are placed at the vertices of a regular pentagon as shown in the figure. The electric potential $(V)$ and the electric field $(\vec{E})$ at the center $O$ of the pentagon due to these five positive charges are:

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