Question

Two equal point charges Q = + root2 uC are placed at each of the two opposite corners of a square and equal
point charges q at each of the other two corners. What must be the value of q so that the resultant force
on Q is zero ?

​

Answer 1

Explanation:

Let a metre the side of the side of the square.The length of a diagonal will be

2

a.The force on the positive charge Q at A due to the positive charge Q at C is F=

4πε

0

1

2a

2

Q

2

and is directed outward,as shown.In order to make net force on Q zero,the resultant of the other two force F

1

and F

2

on Q due to the charges q and q should be equal and opposite to F.Clearly F

1

and F

2

will be directed as shown and for this both q

′

should be negative.

now

F

1

=F

2

=

4πε

0

1

a

2

Qq

since F

1

and F

2

are at right angles, their resultant is

F

12

=

4πε

0

1

a

2

2

Qq

For the equilibrium of Q, we musst have

F=F

12

But Q+

2

μC

∴q=−

2

2

2

μC

=−0.5μC