Answer to Question #107478 in Electricity and Magnetism for Chinmoy Kumar Bera

Question

fore electric charges q=2×10^-8,p=-4×10^-8,r=3×10^-8,s=4×10^-8 are placed at four corners of square of side 1m . calculate the electric potential at centre of square.

Answer 1

$q=2\times 10^{-8},\ p=-4\times 10^{-8}, \ r=3\times 10^{-8},\ s=4\times 10^{-8}$

$a=1\ m$

The potential at the center of the square is equal to the algebraic sum of the potentials at the center due to each of the charges individually.

$V_0= V_1+V_2+V_3+V_4$

$V_1=\frac{kq}{R}=\frac{kq}{a/\sqrt{2}}=\frac{k\sqrt{2}}{a}q$

$V_2=\frac{k\sqrt{2}}{a}p, \ V_3=\frac{k\sqrt{2}}{a}r, \ V_4=\frac{k\sqrt{2}}{a}s$

$V_0=\frac{k\sqrt{2}}{a}(q+p+r+s)$

$V_0=\frac{9\times 10^9\times \sqrt{2}}{1}(2-4+3+4)\times 10^{-8}=636.4 \ V$

Answer: $636.4 \ V$