Question

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

• A. (i) > (ii) > (iii) > (iv)
• B. (ii) > (i) > (iii) > (iv)
• C. (i) > (iii) > (ii) > (iv)
• D. (iv) > (iii) > (ii) > (i)

Answer 1

Answer: (C)

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

$E_{(i)}=\sqrt{(5E{)}^2+(5E{)}^2}=5\sqrt{2}E$
$E_{(ii)}=\sqrt{(3E{)}^2+(3E{)}^2}=3\sqrt{2}E$
$E_{\text{(iii) }}=4E+2E=6E$ and $E_{(iv)}=3E+E=4E$
$\Rightarrow E_{(i)}>E_{(iii)}>E_{(ii)}>E_{(iv)}$