In the following four situations charged particles are equal distance from the origin. Arrange them the magnitude of the net electric field at origin greatest first

Options

A. `(i)gt(ii)gt(iii)gt(iv)`
B. `(ii)gt(i)gt(iii)gt(iv)`
C. `(i)gt(iii)gt(ii)gt(iv)`
D. `(iv)gt(iii)gt(ii)gt(i)`

Answer

c

Explanation

If electric field due to charge `|q|` at origin is `E` then field due to charges `|2q|, |3q|, |4q|` and `|5q|` are respectively `2E, 3E, 4E` and `5E`

`E_((i))= sqrt((5E)^(2)+(5E)^(2))=5sqrt(2)E`,
`E_((ii))= sqrt((3E)^(2)+(3E)^(2))=3sqrt(2)E`,
`E_((iii))= 4E+2E= 6E` and `E_((iv))= 3E+E= 4E`
`implies E_((i))gtE_((iii))gtE_((ii))gtE_((iv))`