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Home » A charge ‘ ‘ is enclosed by a Gaussian spherical surface of radius ‘R’. If, now, radius of the spherical surface is doubled the outward electric flux willA. doubledB. remain sameC. increase four timesD. reduce to half
A charge ‘ q ‘ is enclosed by a Gaussian spherical surface of radius ‘R’. If, now, radius of the spherical surface is doubled the outward electric flux will
A. doubled
B. remain same
C. increase four times
D. reduce to half
Physics
A charge ‘ q ‘ is enclosed by a Gaussian spherical surface of radius ‘R’. If, now, radius of the spherical surface is doubled the outward electric flux will
A. doubled
B. remain same
C. increase four times
D. reduce to half

Correct answer is B.

Method 1: Using Number of Field Lines
– We know that, Electric flux is proportional to number of field lines.
– Form figure, we see that the number of field lines crossing both the spherical surfaces is same.
– Therefore, the flux passing both the surfaces will be same.
Hence correct Option is D

Method 2: Using Gauss Law

– Gauss Law states that, Electric flux \Delta \phi=\frac{\mathrm{q}_{\text {in }}}{\epsilon_{0}}
– Assuming both the spherical surfaces \mathrm{S}_{1} and \mathrm{S}_{2} as gaussian surfaces. From figure, we find that the charge enclosed \left(\mathrm{q}_{\mathrm{in}}=\mathrm{Q}\right. ), same for both the surfaces irrespective of radius.
– Hence, the Flux passing through both surfaces is same.

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