Question

The figure depicts a square box with charges at each vertex. The side length of the box is 2.5 m. The charges are 41 = 1.5 nC, 92 = 3 nC, 43 = 4.5 nC, and 94 = 6 nC. What is the electric potential at point P, located halfway between charges 43 and 44 on the bottom side? 91 92 43 Р

A figure depicts a square box with charges at each vertex. The side length of the box is 2.5 m. The charges are q1=1.5 nC, q2=3 nC, q3=4.5 nC, and q4=6 nC. What is the electric potential at point P, located halfway between charges q3 and q4 on the bottom side?

Answer 1

Ans:90.0V

Solution:

Given,

91 = 1.5nC

72 = 3nc

$q_{3}=4.5nC$

$q_{4}=6nC$

92 au B. А 2,80 ost 2.5m 1:25 D 1.25 C P as 24

From figure,

In $\Delta ADP$ ,

$AP=BP=\sqrt{1.25^2+2.5^2}=2.80m$

The potential at point P is given by,

$V=\frac{1}{4\pi\epsilon_{0}}(\frac{q_{1}}{AP}+\frac{q_{2}}{BP}+\frac{q_{3}}{DP}+\frac{q_{4}}{CP})$

  $=9\times10^9(\frac{1.5\times10^{-9}}{2.80}+\frac{3\times10^{-9}}{2.80}+\frac{4.5\times10^{-9}}{1.25}+\frac{6\times10^{-9}}{1.25})$

  $=9\times10^9\times 10.01\times 10^{-9}$

$=90.0V$