Five positive charges each having charge 
are placed at the vertices of a pentagon as shown in the figure. The electric potential 
and the electric field 
at the center 
of the pentagon due to these five positive charges are:
and 
and 
and 
and 
Text Solution
Verified by ExpertsB
The electric potential at center O is the scalar sum of contributions from all 5 charges.
Each charge is equidistant from center, so 
.
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 
angles.
The vector sum of 5 equally spaced unit vectors is zero, so 
.
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