Electrostatics Question 709
Question: N identical point charges are kept summetrically on the periphery of the circle $ x^{2}+y^{2}=R^{2} $ in xy plane. The resultant electric field at (0, 0, R) is $ E _{1} $ and at (0, 0, 2R) is $ E _{2} $ . The ratio of $ \frac{E _{1}}{E _{2}} $ is
Options:
A) $ \frac{5\sqrt{5}}{4\sqrt{2}} $
B) $ \frac{5}{2} $
C) $ \frac{5}{4} $
D) $ \frac{5\sqrt{5}}{2\sqrt{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ E _{1}=\frac{nkQR}{{{( R^{2}+R^{2} )}^{3/2}}},E _{1}=\frac{nkQ( 2R )}{{{( R^{2}+{{( 2R )}^{2}} )}^{3/2}}} $
$ \therefore \frac{E _{1}}{E _{2}}=\frac{5\sqrt{5}}{4\sqrt{2}} $
