Question

Point charges, +q each is placed at the corners of a triangle, square and regular pentagon. If the sides are a each, the electric field at the center will be:

• A. zero in all three cases
• B. maximum at the center of the pentagon
• C. minimum at the center of the triangle
• D. zero for square and positive for triangle and pentagon

Hint:

Symmetry is a physicist's best friend: Regular shape + Equal charges = Zero field at center.

Answer 1

The Correct Option is A

Step 1: Concept
The electric field is a vector quantity. For a system of charges, the net field at a point is the vector sum of individual fields.

Step 2: Meaning
A regular polygon has high symmetry. When equal charges are placed at all vertices, the field vectors at the geometric center are equal in magnitude and symmetrically distributed in direction.

Step 3: Analysis
In a triangle, square, or pentagon, the symmetry ensures that for every component of an electric field in one direction, there is an equal and opposite component (or set of components) that cancels it out.

Step 4: Conclusion
Mathematically, the vector sum of these fields at the center of any regular polygon with equal vertex charges is always zero. Final Answer: (A)