In the shown figure- there are four point charges each with a charge of -Q and situated the four corners of a square with a side of length D-What is the electric potential the center of the square- -k is the coulomb constant-dfrac-4kQ-D-dfrac-kQ-D - cos 45-dfrac-2kQ-D - cos 45-0dfrac-4kQ-D - cos 45-

Question

Toppr Admin · Accepted Answer

From figure- -xA0- -xA0-x2-x2-D2 -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0-x27F9-x-D-x221A-2-D cos45Electric potential at the point O due to one charge -xA0- -xA0- -xA0- -xA0- V1-kQx-KQDcos45Thus electric potential at the point O due to four charges -xA0- -xA0- -xA0- -xA0- Vo-4V1-4kQ-Dcos45-

In the shown figure, there are four point charges each with a charge of +Q and situated at the four corners of a square with a side of length D.What is the electric potential at the center of the square? (k is the coulomb constant)4kQDkQ(Dcos45)2kQ(Dcos45)04kQ(Dcos45)

From figure, x2+x2=D2 ⟹x=D√2=D cos45Electric potential at the point O due to one charge V1=kQx=KQDcos45Thus electric potential at the point O due to four charges Vo=4V1=4kQ(Dcos45)

From figure, $x^{2} + x^{2} = D^{2}$ $⟹ x = \frac{D}{\sqrt{2}} = D$ $c o s 45$

Electric potential at the point O due to one charge $V_{1} = \frac{k Q}{x} = \frac{K Q}{D c o s 45}$

Thus electric potential at the point O due to four charges $V_{o} = 4 V_{1} = \frac{4 k Q}{(D c o s 45)}$