If coulomb's law were an inverse cube law F ∝ 1 r 3 , would Gauss's still hold.

No, Gauss law can not be applied if the coulombs' law were not inverse square law because in that case, flux depends upon distance, which is not true. So Gauss's law will not be true if coulomb's law was not inverse square law .In Gauss's law, flux through a closed surface depends upon the charge present inside and not on the shape or size of the Gaussian surface. E = k q r 3 Taking surface integral of this electric field to find flux gives : Φ = 4 πkq r

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 8

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If the radius of the gaussian surface enclosing a charge is halved, how does the electric flux through the gaussian surface change?

Important Questions on Gauss' Law and its Application

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 9

An electric charge

Q

is distributed on a thin conducting spherical shell uniformly. What is the electric field at the centre ? If the shape of the shell is changed will the result be different? What will happen if the spherical shell is nonconducting?

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 10

Draw graphs showing the variations of the electric field and potential due to a spherical shell .

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 10

Draw graphs showing the variations of the electric field and potential due to a uniformly charged sphere with distance from its centre.

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 11

Explain why a soap bubble expands in volume when given a charge.

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 12

Explain why charges accumulate more at sharp points of a conductor.

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 13

Two spheres of different radii are connected together. They are given a charge. Find the relation between the surface charge density and radii of the two spheres.

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A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 14

If coulomb's law were an inverse cube law