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Question

S1,S2,S3 are three concentric spherical shells as shown in figure. S1 and S2 have charge 4Q and 8 Q respactively Whereas S3 is unchanged. Find the ratio of the flux passing through S1 to that through S3
1268887_664ce67b8d5d47caafd6c40c7443f1a0.png

A
1 : 3
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B
1 : 2
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C
2 : 1
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D
1 : 6
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Solution

The correct option is A 1 : 3

Step 1: Draw figure [Ref. Fig.]
Given, Charges on shells:
QS1=4Q, QS2=8Q

Step2: Applying Gauss law
If a charge q is enclosed inside a closed surface then flux through that surface =q0
So, ϕS1=QS10=4Q0

From figure, charges QS1 and QS2 are enclosed by shell S3
So, ϕS3=Q inside S30=8Q+4Q0

Step 3: Ratio of flux
ϕS1ϕS3=4Q08Q+4Q0=412=13

Hence the ratio of flux passing through S1 to that through S3 is 1:3

Option (A) correct.

2111168_1268887_ans_a0d9735863b74204ad7a6f64c264ec4c.png

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