Ten charges (5 of them are +q each & other five are –q each) are placed randomly on the circumference of a circle. The radius of the circle is R. The electric potential at the centre of this sphere due to these charges will be
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The electric potential at a point due to a point charge is given by V = kq/r, where r is the distance from the charge to the point. The potential is a scalar quantity, so the total potential at the center is the algebraic sum of the potentials due to all individual charges.
For charges on the circumference, the distance from each charge to the center is the radius R. Therefore, the potential from a single +q charge is and from a single -q charge is .
Since there are five positive and five negative charges, their contributions cancel each other out exactly. The total potential is:
This result is independent of the positions of the charges on the circle because potential is a scalar and depends only on the distance and the charge magnitude.
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