Four point charges q, -2q, -q and 2q are placed at points (0,0,0) m , `(sqrt(2), 0,0) m, (sqrt(2), sqrt(2),0)m " and " (0, sqrt(2) , 0)` m respectively . The electric field at point `((1)/(sqrt2), (1)/(sqrt2),0) m " is " (q=1muC)`

Options

A. `18xx10^3 N//C`
B. `36xx10^3 N//C`
C. `18sqrt(5) xx10^3 N//C`
D. `18sqrt(3)xx10^3N//C`

Answer

C

Explanation

Use `vecE=vecE_1 + vecE_2+vecE_3 +….. " and " E=(KQ)/(r^2)`

Given co-ordinates of point
A=(0,0,0)
`B=(sqrt(2), 0,0)`
`C=(sqrt(2), sqrt(2) ,0)`
`D=(0, sqrt(2), 0)`
`O=(1/sqrt2,1/sqrt2,0)`
`|E_A|=|E_C|=(1)/(4piepsi_0).(q)/(r^2) = (9xx10^9)/(1) xx1xx10^(-6) = 9xx10^3 N//C`
`|E_B|=|E_D|=(1)/(4piepsi_0) .(2q)/(r^2) = 18xx10^3 N//C`

`|vecE_A+vecE_C|=18xx10^3 N//C`
`|vecE_B + vecE_D| = 36xx10^3N//C`
`E("net") = sqrt((36xx10^3)^2+(18xx10^3)^2)`
`=18sqrt(5)xx10^3N//C`