Question

three point charges +1 nC +2nC and -3nC are placed in two adjacent vertices and in the center if a square with 3m ling sides. find electric field (magnitude and direction) and electric potential (magnitude and sign) in the empty vertices of the square. find total potential energy of the interaction between charges . find force of interaction between the charges in the vertices.

Answer 1

Charges q = 1 x10 ^-9 C

            q ' = 2 x10 ^-9 C

            q " = -3 x10 ^-9 C

Side of the square a = 3 m

Empty vertice nearar to +1nC :

Electric field at empty vertic due to charge q is E =Kq /a ²

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

Substitute values you get E = 0.9988 N/C

                                          = 1 N/C

Electric field at empty vertic due to charge q ' is E =Kq ' /r ²

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

            r = distance of the empty corner from charge q '

              = length of diagonal = a

              = 1.414 x 3 m = 4.242 m

Substitute values you get E ' = 0.9988N/C

Electric field at empty vertic due to charge q " is E =Kq " /(r/2) ²

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

            r = distance of the empty corner from charge q '

              = length of diagonal = a

              = 1.414 x 3 m = 4.242 m

Substitute values you get E " = 5.99 N/C

E ' and E " are opposite to each other.

So, resultant of these two is E1=E ' - E "

                                              = 4.9963 N/C

                                               ~ 5 N/C

E and E1 are in 135 ^o .

Therefore resultant field at empty corner Er = [E ²+E1 ²+2EE1 cos 135]

                                                               = [ 1 ² + 5 ² + 2(1)(5)(-0.7071)]

                                                               = 4.35 N/C

Electric potential :

Electric potential at empty vertic due to charge q is V =Kq /a

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

            a = distance of the empty corner from charge q

              = 3 m

Substitute values you get V ~ 1 volt

Electric potential at empty vertic due to charge q ' is V' =Kq ' /r

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

            r = distance of the empty corner from charge q '

              = length of diagonal = a

              = 1.414 x 3 m = 4.242 m

Substitute values you get V ' = 2.121 volt

Electric potential at empty vertic due to charge q " is V ' =Kq " /(r/2)

Where K = Coulomb's constant = 8.99 x10 ⁹ Nm ²/ C ²

            r = distance of the empty corner from charge q '

              = length of diagonal = a

              = 1.414 x 3 m = 4.242 m

Substitute values you get V " = - 12.73 volt

Potential at empty corner due to three charges q , q' q " is = V + V ' + V "

                                                                                     = -9.609 volt.

Similarly you calculate electric field and potential at other empty corner.

total potential energy of the interaction between charges

U = [-Kqq ' / a]+ [-Kqq " / (r/2)]+[-Kq 'q"/(r/2)]