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If Coulomb's law involved 1/r^3 instead ...

If Coulomb's law involved `1/r^3` instead of `1/r^2`, would Gauss's law still be true?

A

there were magnetic monopoles

B

the inverse square law were not exactly true

C

the velocity of light were not a universal constant

D

None of the above

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The correct Answer is:
B
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Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1) Q_(2)//4pi epsilon_(0) r_(2) , where r is the distance between their centers? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of 1//r^(2) ), would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

Gauss's law part-1

Gauss's law part-2

If It is 1/r^2.5 in place of 1/r^2 , would Gauss's law still hold?

Which of the following statement(s) is/are correct? If the electric field due to a point charge varies as r^(-2.5) instead of r^(-2),then the Gauss law will still be valid. The Gauss law can be used to calculate the field distribution around an electric dipole. If he electric field between two point charges is zero somewhere,then the sign of the two charges is the same. The work done by the external force is moving a unit positive charge from point A at potential "V_(A)" to point B at potential "V_(B)" is,(V_(B)-V_(A))

Assertion: Column's law can be derived from Gauss's law. Reason: Gauss's law can be derived from Coulombs law.

The Bohr model for the H-atom relies on the Coulomb's law of electrostatics . Coulomb's law has not directly been varified for very short distances of the order of angstroms. Suppos-ing Coulomb's law between two oppsite charge +q_(1),-q_(2) is modified to |vec(F)|=(q_(1)q_(2))/((4piepsilon_(0))r^(2))1/r^(2),rgeR_(0) =(q_(1)q_(2))/((4piepsilon_(0))r^(2))1/R_(0)^(2)(R_(0)/r)^(epsilon), rleR_(0) Calculate in such a case , the ground state enenergy of H-atom , if epsilon 0.1,R_(0)=1Å

DC PANDEY-ELECTROSTATICS-Check point 1.5
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  4. Flux coming out from a positive unit charge placed in air, is

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  5. If the electric flux entering and leaving an enclosed surface respecti...

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  6. Charge of 2 C is placed at the centre of a cube. What is the electric ...

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  7. For a given surface the Gauss's law is stated asoint vecE.dvecA=0. Fro...

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  8. The total electric flux emanating from a closed surface enclosing an a...

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  9. The inward and outward electric flux for a closed surface in unit of N...

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  10. If the flux of the electric field through a closed surface is zero , ...

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  11. Consider the charge configuration and a spherical Gaussian surface as ...

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  12. q(1),q(2),q(3) and q(4) are point charges located at point as shown in...

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  13. The Gaussian surface for calculating the electric field due to a charg...

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  14. If Coulomb's law involved 1/r^3 instead of 1/r^2, would Gauss's law st...

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  15. Two parallel infinite line charges with linear charge densities +lambd...

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  16. An infinite line charge produces a field of 9xx10^(4) NC at a distance...

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  17. A charge of 17.7 xx 10^(-4)C is distributed uniformly over a large she...

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  18. From what distance should a 100 eV electron be fired towards a large m...

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  19. If the field near the earth's surface is 300V m^(-1) directed downward...

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  20. A thin spherical shell of metal has a radius of 0.25 m and carries a c...

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