Two concentric spherical shell's of radius R1 & R2 have q1 & q2 charge respectively as shown in figure. How much charge will flow through key k when it is closed :-
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Options
1. Image not present
2. Image not present
3. Image not present
4. Image not present

Asked by devanshmalhotra2609 | 9th Jan, 2016, 11:05: PM

Expert Answer:

Two concentric spherical shell of radius R1 & R2 have q1 & q2 charge respectively.(where, R2 > R1)
Now, the inner shell is grounded which implies that the inner shell will come at zero potential.
From the given figure, when key is closed and object is grounded it potential reduced to zero.
q1 induces -q1 on the inner surface of outer sphere and +q1 on outer surface of outer sphere
Potential of inner sphere = Potential due to charge on inner surface + Potential due charge on outer surface = 0
begin mathsize 12px style straight V subscript straight A equals fraction numerator straight q subscript 1 over denominator 4 πε subscript 0 straight R subscript 1 end fraction minus fraction numerator straight q subscript 1 over denominator 4 πε subscript 0 straight R subscript 2 end fraction plus fraction numerator straight q subscript 1 plus straight q subscript 2 over denominator 4 πε subscript 0 straight R subscript 2 end fraction equals 0 rightwards double arrow straight q subscript 1 equals negative straight q subscript 2 open parentheses straight R subscript 1 over straight R subscript 2 close parentheses Which space implies space that space straight a space charge space straight q subscript 2 open parentheses straight R subscript 1 over straight R subscript 2 close parentheses space has space been space transferred space to space earth space leaving space negative space charge space on space inner space sphere Since space straight R subscript 2 space greater than space straight R subscript 1 comma space charge space flow space will space be space positive rightwards double arrow space straight q subscript 2 open parentheses fraction numerator straight R subscript 2 minus straight R subscript 1 over denominator straight R subscript 2 end fraction close parentheses space greater than space 0 end style
Hence, Correct option is 3
 
The Concept of concentric shell is well explained in NCERT Text book Class XII part I page no. 39 and 40.
If you have any conceptual doubts in it, we will glad to clear it.

Answered by Priyanka Kumbhar | 12th Jan, 2016, 11:44: AM