Three charges q, sqrt{2}q,and 2q are placed a | vedclass

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Question

(B) The electric potential $V$ at a point due to a system of point charges is the algebraic sum of the potentials due to each charge individually: $V

Vedclass · Accepted Answer

$\frac{4kq}{a}$

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(B) The electric potential $V$ at a point due to a system of point charges is the algebraic sum of the potentials due to each charge individually: $V = \sum \frac{kq_i}{r_i}$.In square $ABCD$ of side $a$:$1$. The distance from $A$ to $D$ is $r_A = a$.$2$. The distance from $B$ to $D$ is the diagonal of the square,$r_B = a\sqrt{2}$.$3$. The distance from $C$ to $D$ is $r_C = a$.The potential at $D$ is $V_D = \frac{kq_A}{r_A} + \frac{kq_B}{r_B} + \frac{kq_C}{r_C}$.Substituting the values: $V_D = \frac{kq}{a} + \frac{k(\sqrt{2}q)}{a\sqrt{2}} + \frac{k(2q)}{a}$.$V_D = \frac{kq}{a} + \frac{kq}{a} + \frac{2kq}{a} = \frac{kq}{a}(1 + 1 + 2) = \frac{4kq}{a}$.

Three charges $q, \sqrt{2}q$,and $2q$ are placed at the corners $A, B$,and $C$ respectively of a square $ABCD$ of side length $a$. Find the electric potential at point $D$.

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