First slide

Electric field

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.

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 lql at origin is E, then electric field due to charges 12ql, 13ql, 14ql and 15ql are respectively 2E, 3E, 4E and 5E.
$E_{(i)} = \sqrt{(5 E)^{2} + (5 E)^{2}} = 5 \sqrt{2} E E_{(ii)} = \sqrt{(3 E)^{2} + (3 E)^{2}} = 3 \sqrt{2} E E_{(iii)} = 4 E + 2 E = 6 E and E_{(iv)} = 3 E + E = 4 E \Rightarrow E_{(i)} > E_{(iii)} > E_{(ii)} > E_{(iv)}$

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