Question

A charge of 1.054 x 10^-5 C at each corner of a square with 0.1 m on a side. Calculate the force on the charge at the upper right corner (191 N). b) With that Charge Absent, Calculate the electric field at that position due to the presence of the three other charges

Answer 1

a) Force on a charge 1w by a charge q1 separated by a distance r is given by

Let us draw the charge arrangement.

We need to find the force on q due to charges at 1, 2, 3

Force on q due to charge at 1 is given by,

Similarly, force on q due to charge 3 is,

Distance between charge q and 2 is

Hence, force on charge q due to charge at 2 is given by,

From the figure it is evident that, F1 and F3 are directed perpendicular to each other and hence their resultant is,

This vector is directed along the line of F2.

Hence, net resultant force on q is,

b) Electric field at a distance r due to a point charge q is given by,

Electric field at the upper right hand corner due to a charge at 1 is,

Electric field at the upper right hand corner due to a charge at 3 is,

Distance between the upper right hand corner and the charge at 2 is,

Hence, field due to charge at 2 is given by

Similar to the previous part, directions of E1, E2, E3 are similar to that of F1, F2 and F3.

So resultant of E1 and E3 is,

Resultant electric field is,