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The following question appeared in JEE Advanced 2014.

Let $$E_{1}(r )$$, $$E_{2}(r )$$ and $$E_{3}(r )$$ be respectively electric fields at a distance $$r$$ from a point charge $$Q$$, an infinitely long wire with constant linear charge density $$\lambda$$, and an infinite plane with uniform surface charge density $$\sigma$$. If $$E_{1}(r_{0})=E_{2}(r_{0})=E_{3}(r_{0})$$ at a given distance $$r_{0}$$, then

$$(a) Q=4\sigma\pi r_{0}^{2}$$

$$(b) r_{0}=\displaystyle\frac{\lambda}{2\pi\sigma}$$

$$(c ) E_{1}\left( \displaystyle\frac{r_{0}}{2}\right)=2E_{2}\left( \displaystyle\frac{r_{0}}{2}\right)$$

$$(d) E_{2}\left( \displaystyle\frac{r_{0}}{2}\right)=4E_{3}\left( \displaystyle\frac{r_{0}}{2}\right)$$

The answer is given as $$(c )$$ according to the official answer key.

However I feel that there can be two possible answers to this question.If you assume the plane to be made of non-conducting material then the answer is $$(c )$$. However if you assume that it is conducting then the answer obtained is $$(a)$$, $$(b)$$ and $$(c )$$. I also feel that as it has not been mentioned in the question both assumptions are valid and both answers should be marked correct.

Note by Karthik Kannan
2 years, 9 months ago

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when nothing is given, don't we assume it non-conducting rather than conducting.. and that way, even you know the answer is (C). just think, it talks of a wire and a point charge, where does it have to do anything with taking a conducting plane.. but, yes, if it was conducting you would be right.. · 2 years, 9 months ago

Usually in multicorrect questions I get pretty nervous if I get only one option correct. So if I had given the test, I too would have assumed it to be conducting just by seeing that 3 options matched! (I'm not saying that only one option can never be correct in multicorrect questions, but usually there are more than one correct options)

Tough luck! · 2 years, 9 months ago

Another ambiguous one is q.59 Paper 1 code 1. The question doesn't specify that the mentioned plane is XY anywhere. · 2 years, 9 months ago

You people can thrash me for what I'm gonna say but... Give me one reason why the field should be different if the sheet is conducting? Its a sheet, its infinitely thin, even if you distribute the "internal" charge in the conductor, it will superimpose onto itself & cancel... then why should it matter whether conducting or not o_O? · 2 years, 9 months ago

& I guess they have explicitly used "plane" to remove ambiguity, if what you people are saying is correct, doesn't it mean the field due to a point charge is gonna be different, because that point charge is conducting? say a conducting metal ion particle?? · 2 years, 9 months ago

@Karthik Kannan , Did you send them an e-mail about this issue? · 2 years, 9 months ago

No, I haven't. I was wondering whether I should. · 2 years, 9 months ago

There's no harm in sending them an email. If they consider your appeal, well and good! If they don't, your score won't be affected in anyway ;) · 2 years, 9 months ago

Looks like I have been really lucky with the two recent problems shared by Parth, Karthik and Jatin. I too was puzzled in regards with the formula of electric field to be used. Since nothing was mentioned, I went off with the non-conducting case. · 2 years, 9 months ago

I too answered ABC · 2 years, 9 months ago