Question

Equal charges `q` are placed at the four corners `A,B,C,D`of a square of length `a`. The magnitude of the force on the charge at `B` will be
A. `(3q^(2))/(4piepsilon_(0)a^(2))`
B. `(4q^(2))/(4piepsilon_(0)a^(2))`
C. `((1+2sqrt(2))/(2))(q^(2))/(4piepsilon_(0)a^(2))`
D. `(2+(1)/(sqrt(2)))(q^(2))/(4piepsilon_(0)a^(2))`

Answer 1

Correct Answer - c
After following the guidelines mentioned above
`F_("net")=F_(AC)+F_(D)=sqrt(F_(A)^(2)+F_(C )^(2))+F_(D)`
Since `F_(A)=F_(C)= (kq^(2))/(a^(2))` and `F_(C )= (kq^(2))/((asqrt(2))^(2))`

`F_(n et)=(sqrt(2)kq^(2))/(a^(2))+(kq^(2))/(2a^(2))=(kq^(2))/(a^(2))=(kq^(2))/(a^(2))(sqrt(2)+1/2)`
`=(q^(2))/(4piepsilon_(0)a^(2))((1+2sqrt(2)))/(2)`