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Gauss's theorem...

Gauss's theorem

A

does not hold, if the closed surface enclosed a discrete distribution of charges

B

does not hold, if the closed surface encloses, a line, a surface or a volume charge distribution

C

holds, if the surface encloses a point charge only

D

holds irrespective of the form in which charges are enclosed by the closed surface.

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The correct Answer is:
D
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A physics teacher explains Gauss's theorem in electrostatics and Gauss's theorem in magnetism to his students in a class. He tells them that total normal electric flux over a closed surface in vacuum is phi_e=(Q)/(in_0) , where Q is algebraic sum of charges inside the surface. Further, total normal magnetic flux over a closed surface in vacuum is always zero. The teacher emphasises that this is because in magnetism, poles always exist in unlike pairs of equal strengh, i.e., isolated magnetic poles called monopoles do not exist. Read the above passage and answer the following questions: (i) What are the implications of Gauss's theorem in magnetism in day to day life? (ii) Two magnetic dipoles of moments 5Am^2 and 3Am^2 oriented along opposite directions are enclosed in a surface. What is total normal magnetic flux over this surface? (iii) Two point charges +4q and -q are enclosed in a surface in vacuum, and third charge 5q lies outside the surface. What is total normal electric flux over the surface?

(a) Use Gauss's theorem to find the electric field due to a uniformly charged infinitely Iarge plane thin sheet with surface charge density. Sigma (b) An infinitely large thin plane sheet has a uniform surface charge density + sigma . Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point , distant r, in front of the charged plane sheet.

The Gauss' theorem for gravitational field may be written as

A : Gauss theorem is applicable on any closed surface. R : In order to find the value of electric field due to a charge distribution, Gauss' theorem should be applid on a symmetrical closed surface.

A charge q is situated at the centre of an imaginary hemispherical surface, as shown in figure. Using gauss's theorem and symmetry considerations, determine the electric flux due to this charge through the hemisphere surface.

NIKITA PUBLICATION-ELECTROSTATICS-Multiple Choice Questions
  1. Gauss's theorem is

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  2. A Gaussian surface enclosed no charge. Which of the following is true ...

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  3. Gauss's theorem

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  4. The total normal electric induction over a closed surface is equal to ...

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  5. If the charge lies outside the closed surface then by Gauss's theorem,...

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  6. Gauss's theorem is true for any point charge situated any where

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  7. If negative charge is enclosed by the surface, then the T. N. E. I. ov...

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  8. The solid angle substended at any point inside the surface due to smal...

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  9. The electric charges of +9C, -10C and -8C are enclosed anywhere by a c...

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  10. If infinite parallel plane sheet of a metal is charged to charge densi...

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  11. Electric intensity at a point near a charged sphere of charge q is giv...

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  12. A cylinder of length L has a charge of magnitude q. The electric inten...

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  13. The electric intensity at a point near a charged conductor of surface ...

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  14. A sphere of radius R has a charge density sigma. The electric intensit...

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  15. A charge +q is placed at the mid point of a cube of side L. The electr...

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  16. The electric flux through a hemispherical surface of radius R placed i...

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  17. Electric field intensity at a point is inversely proportional to cube ...

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  18. Electric intensity at a point due to a charged cylinder of infinite le...

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  19. The electric field inside a spherical shell of uniform surface charge ...

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  20. As one penetrates uniformly charged conducting sphere,what happens to ...

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