Five positive charges each having charge $q$ are placed at the vertices of a 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:

Question

Five positive charges each having charge

q

are placed at the vertices of a 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:
Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The

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Correct answer: B. V= 5 q 4 π _ o r and E =0

The electric potential at center O is the scalar sum of contributions from all 5 charges.
Each charge is equidistant from center, so

V = 5 cdot \frac{kq}{r} = \frac{5q}{4\pi\epsilon_0 r}

.
The electric field is a vector sum of field vectors from all 5 charges.
Due to 5-fold rotational symmetry of a regular pentagon, the 5 field vectors point radially outward from center, equally spaced at 72° angles.
The vector sum of 5 equally spaced unit vectors is zero, so

\vec{E} = 0

.

Five positive charges each having charge q are placed at the...

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