Define the term electric potential due to a point charge. Calculate the electric potential at the centre of a square of side $\sqrt{2} m,$ having charge 100 μC, – 50 μC, 20 μC and – 60 μC at the four corners of the square.

Solution

Electric potential at a point is defined as the amount of work required to carry a unit positive charge with zero acceleration from infinity to that particular point under consideration in electric field, against the electrostatic forces.

Side of the square,a =

\sqrt{2} m

Charge, q_{A =} 100 μC

Charge, q_{B =}– 50 μC
Charge, q_C= 20 μC
Charge, q_D = – 60 μC

Diagonal of the square, AC =

\sqrt{{(\sqrt{2})}^{2} + {(\sqrt{2})}^{2}} = 2 m

Distance of any charge from centre O = AC/2 = 1m.
Potential at the centre of the square,

V = \frac{k q}{r}

∴ V = 9 \times 10^{9} [\frac{100 \times 10^{- 6}}{1} - \frac{50 \times 10^{- 6}}{1} + \frac{20 \times 10^{- 6}}{1} - \frac{60 \times 10^{- 6}}{1}] = 9 \times 10^{9} \times 10^{- 6} \times 10

V = 9 \times 10^{4} V .

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Define the term electric potential due to a point charge. Calculate the electric potential at the centre of a square of side $\sqrt{2} m,$ having charge 100 μC, – 50 μC, 20 μC and – 60 μC at the four corners of the square.

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Define the term electric potential due to a point charge. Calculate the electric potential at the centre of a square of side $\sqrt{2} m,$ having charge 100 μC, – 50 μC, 20 μC and – 60 μC at the four corners of the square.