Question

Shown above are four point charges each with a charge of $+Q$ and situated at the four corners of a square with sides of length D.
What is the electric potential at the center of the square? (k is Coulomb constant.)

• A. $\frac{4kQ}{D}$
• B. $\frac{4kQ}{\left(D\cos {45}^{\circ }\right)}$
• C. $\frac{2kQ}{\left(D\cos {45}^{\circ }\right)}$
• D. $\frac{kQ}{\left(D\cos {45}^{\circ }\right)}$
• E. $0$

Answer 1

The correct option is B $\frac{4kQ}{\left(D\cos {45}^{\circ }\right)}$

Let r be the distance of each charge from center of the square ,

then $r^2+r^2=D^2$ ,

or $r=D/\sqrt{2}$ ,

q

electric potential at he center of square due to four charges , each of $+Q$ at the four corners ,

$V=k(Q/r+Q/r+Q/r+Q/r)$ ,

or $V=k\left(4Q\right)/r=4kQ/\left(D/\sqrt{2}\right)$ ,

or $V=4KQ/\left(D\cos {45}^o\right)$ (because $\cos {45}^0=1/\sqrt{2}$)