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

E M B I B E

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

MEDIUM

12th West Bengal Board

IMPORTANT

Earn 100

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

Important Questions on Gauss' Law and its Application

MEDIUM

12th West Bengal Board

IMPORTANT

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.

HARD

12th West Bengal Board

IMPORTANT

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

(F \propto \frac{1}{r^{3}}),

would Gauss's still hold.

EASY

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 15

If a Gaussian surface does not include any charge, does it necessarily mean that electric field is zero at all points on the surface.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 1

State Gauss's theorem. Hence, show that the charges on a spherical shell practically produce their field at an external point in such a way that they may be supposed to be concentrated at its centre.

HARD

12th West Bengal Board

IMPORTANT

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

Apply Gauss's law to find the intensity of electric field at a point due to (ii) uniformly charged thin spherical shell.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 4

Derive Gauss's law from Coulomb's law.

HARD

12th West Bengal Board