NEET Class neet Answered

Q 30 Option 3

Asked by manasvijha | 17 Apr, 2019, 07:54: AM

Expert Answer

Potential at middle sphere is zero because it is earthed.

Potential at middle sphere is due to charge Q of innermost sphere, charge Q of outer sphere and

due to charges transferred by earth due to earthing.

Potential at middle sphere due to charge Q of innermost sphere =

begin mathsize 12px style fraction numerator Q over denominator 4 pi epsilon subscript o left parenthesis 2 r right parenthesis end fraction end style

.......................(1)

Potential at middle sphere due to charge Q of outer sphere =

begin mathsize 12px style fraction numerator Q over denominator 4 pi epsilon subscript o left parenthesis 3 r right parenthesis end fraction end style

..........................(2)

Potential at middle sphere due to charges on innermost sphere and outer sphere is obtained

as sum of eqn.(1) and eqn.(2) =

begin mathsize 12px style fraction numerator Q over denominator 4 pi epsilon subscript o end fraction open parentheses fraction numerator 1 over denominator 2 r end fraction plus fraction numerator 1 over denominator 3 r end fraction close parentheses space equals space fraction numerator begin display style 5 over 3 end style Q over denominator 4 pi epsilon subscript o open parentheses 2 r close parentheses end fraction end style

....................... (3)

Since the middle sphere is earthed, to make the potential of middle sphere as zero,

earth has to transfer -(5/3)Q to middle sphere as per eqn.(3)

Middle sphere has already +Q as induced charges due to charge on innermost sphere.

Hence net charge on middle sphere Q -(5/3)Q = - (2/3)Q

Answered by Thiyagarajan K | 17 Apr, 2019, 12:56: PM

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