Sometimes, even 'infinite' helps!

Two point charges, q q and q -q are separated by a distance l l , both being located at a distance l 2 \frac{l}{2} from the infinite conducting plane.

If the modulus of the vector of the electric force acting on each charge is given by

( A B 1 ) q 2 C π ϵ 0 l 2 \large \frac{(A\sqrt B-1)q^2}{C\pi\epsilon_0l^2}

and the magnitude of electric field strength vector at the midpoint between these charges is given by

D ( 1 1 E F ) ( q π ϵ 0 l 2 ) \large D(1-\frac{1}{E\sqrt F})(\frac{q}{\pi\epsilon_0l^2}) where A , B , C , D , E , F A,B,C,D,E,F are positive integers with B , F B,F square-free. Enter your answer as A × B × C × D × E × F A\times B\times C\times D\times E\times F


The answer is 1600.

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1 solution

Suhas Sheikh
Jun 13, 2018

Easy enough Use method of images To construct an equivalent charge assembly A square with side length l And adjacent corners being occupied by unlike charges (magnitude remains q) This can be done as the infinite plane can be used create image charges of the positive and negative charges on the other side of the plane

Rest is easy computation You will get A=2 B=2 C=8 D=2 E=5 F=5 Giving you 1600 as the answer

Typo: Electric field shouldn't have the term "q^2" (only q) Kindly change it

Yeah, I changed it. Thanks.

Shreyansh Mukhopadhyay - 2 years, 12 months ago

Nice question buddy.

Md Zuhair - 2 years, 12 months ago

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Thanks. @Md Zuhair , have you given NSEP? I am just trying to qualify the first stage. I don't think there are chances of being qualified in class 10 but I want to give it being prepared. Can you tell me about the paper pattern and which topics are more important as there is very less time left ( in November) ?

Shreyansh Mukhopadhyay - 2 years, 12 months ago

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You are in 10th!!! Awesome.... Well u can check out previous year papers.

Md Zuhair - 2 years, 12 months ago

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