A charges Q is placed at each of the two opposite corners of a square. A charge q is placed to each of the other two corners. If the resultant force on each charge q is zero, then

Options

A. `Q=-2sqrt2q`
B. `Q=sqrt2q`
C. `Q=-sqrt2q`
D. Q=-2q

Answer

A

Explanation

The force on charge is zero, therefore
`F_(qQ) cos 45^@+F_(qQ) cos 45^@ +F_(Q Q)=0`

`2F_(qQ)1/sqrt2+F_(Q Q)=0`
`1/(4piepsilon_0)[(qQ)/a^2 sqrt2 + (Q Q)/(2a^2)]=0`
`therefore Q=-2sqrt2q`