Question

Point charges q1=+2.00μCq1=+2.00μC and q2=−2.00μCq2=−2.00μC are placed at adjacent corners of a square for which the length of each side is 4.00 cmcm. Point aaa is at the center of the square, and point b is at the empty corner closest to q2q2. Take the electric potential to be zero at a distance far from both charges.

A point charge q3q3q_3 = -6.00 μCμC moves from point aaa to point bbb. How much work is done on q3q3 by the electric forces exerted by q1q1 and q2q2?

Express your answer with the appropriate units.

Answer 1

We have the arrangement of charges as shown in fallowing figure,

we have,

charge at Corner C and

charge at corner D

length of side of square = .

using Pythagoras theorem we get,

distance between charge at corner C and point b diagonal of square

distance between charge at corner C and square center 'a' Diagonal of square 2 =

distance between charge at corner D and point 'b' length of side of square =

distance between charge at corner D and square center 'a' Diagonal of square 2 =

Now we need to calculate the net electric potentials at points 'a' and 'b' due to charges and .

consider point a,

electric potential at point 'a' due to charge is given as,

where   

and

electric potential at point 'a' due to charge is given as,

   where

So net electric potential at point 'a' due to both charges   and . is given as,

Since we get,

Using given we get net electric potential at point 'a' as,

Similarly Consider point 'b',

electric potential at point 'b' due to charge is given as,

where

and

electric potential at point 'b' due to charge is given as,

   where

So net electric potential at point 'b' due to both charges  ​​​​​​​ and . is given as,

Since and   we get,

Using given we get net electric potential at point 'b' as,

used

where ​​​​​​​permittivity of vacuum =

In electrostatics the work done to move a charge   form point P at electric potential to point Q at electric potential is given as,

So, as per above relation,

the work done to to move a charge   form point 'a' at electric potential to point 'b' at electric potential will be given as,

Since as we found earlier we get,

Using earlier calculated value of and we get,

​​​​​​​

So, the work done on charge by charges   and . is given as,

(expressed in 3 significant digits )