First slide

Electric field

Question

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

Moderate

A

(i) > (ii) > (iii) > (iv)
B

(ii) > (i) > (iii) > (iv)
C

(i) > (iii) > (ii) > (iv)
D

(iv) > (iii) > (ii) > (i)

Solution

If electric field due to charge $| q |$ at origin is E then electric field due to charges $| 2 q |, | 3 q |, | 4 q | and | 5 q |$ are respectively 2E,3E, 4E and 5E
$\begin{array}{l} E_{(i)} = \sqrt{(5 E)^{2} + (5 E)^{2}} = 5 \sqrt{2} E \\ E_{(ii)} = \sqrt{(3 E)^{2} + (3 E)^{2}} = 3 \sqrt{2} E \\ E_{(iii)} = 4 E + 2 E = 6 E and E_{(iv)} = 3 E + E = 4 E \\ \Rightarrow E_{(i)} > E_{(iii)} > E_{(ii)} > E_{(iv)} \end{array}$

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