Gauss Law Questions and Answers

28 A ball having a charge 100e is placed at the centre of a hollow spherical shell which has a net charge of 20e What is the charge on the shell s outer surface a 80e b 20e c 100e d 120e 37 F

1 Which of the following statements is incorrect for Gauss s law a Gaussian surfaces are arbitrary surfaces on which the electric field magnitude can be written as a constant b Gauss s law is the average of the total loads inside the Gaussian surface drawn c Gauss s law calculates the electric field magnitude but not the electric field direction D For Gauss s law to be valid space must be electrically permeable to The integral expression of Gauss s law is the expression of a special case of the fundamental divergence theorem Answer option b Please explain why the answer is b

Figure shows a cylindrical Gaussian surface for an infinitely long thin straight wire of unifor linear charge density Answer the following i For which surface is the electric flux zero ii Over which surface is E zero iii Over which surface is constant iv Over which surface does E change

A positive charge Q is uniformly distributed along a circular ring of radius R A small test charge q is placed at the center of the ring then R q Z Q i If q 0 and is displaced away from the center in the plane of the ring it will be pushed back towards the centre ii If q 0 and is displaced away from the centre in a plane of the ring it will never return to the centre and will continue moving till it hits the ring iii If q 0 it will perform SHM for small displacement along the axis iv q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q 0 Mark the correct option A i and iv are correct B ii and iii are correct C all are correct

Example 1 11 The electric field components in Fig 1 27 are E x E E 0 in which a 800 N C m 2 Calculate a the flux through the cube and b the charge within the cube Assume that a 0 1 m y n a a R X

38 If charge is distributed uniformly in xy plane with charge density to in first quardrant and o in remaining three quadrants then work done by electric field in moving a point charge q from 0 0 d to 0 0 2d is a oqd b d q 4F c oqd d aq

As seen in the figure a point Q charge is placed in the center of an uncharged conductor with inner radius ri and outer radius r2 Using Gauss s law a r r b ri r r2 c Calculate the electric field in regions r2 r Q

Find electric field everywhere on a plane containing the borders of two parallel half planes extending in opposite directions Distance between the half planes is d and they have uniform surface charge density o each Angle between the plane and the half planes is 0 Ito outside O at all paints between half plave 11 of side gido I carries uniform charge on all of it

94 point ges points as shown in figure S is the spherical Gaussian surface of radius R Which of the following is true according to Gauss s law 9 92 R 93 S 94 280 1 E E E A E E A 91 92 93 2 E E E dA 91 92 93 E0 3 4 E E E E A 91 92 93 Eo

D Same case for cube or cuboid e are 6 faces An infinitely large plate of width b is placed in horizontal x y plane A point charge q is placed b 2 symmetrically at a distance of perpendicular to plane of this plate as shown Find electric flux passing through this plate 1 90 E0 3 Zero 22 b b 2 b 2 2 4 9 2 0 90 E0

Charge is distributed uniformly in some space The net flux passing through the surface of an imaginary cube of side a in the space is The net flux passing through the surface of an imaginary sphere of radius a in the space will be 3 1 47 2 3 2 3 4 6 47 3

The electric field near the centre of a uniformly charged nonconducting disc is E If the nonconducting disc is now replaced by a conducting disc with the charge same as before the new electric field at the same point is 1 2 3 4 2E E E 2 None of these

A hollow cylinder has a charge q coulomb within it If o is the electric flux in units of voltmetre associated with the curved surface B the flux linked with the plane surface A in units of voltmetre will be charge is symmetrically placed within it AIPMT Prelims 2007 1 3 C 9 9 ola B 2 4 q 2 0 elm A 3

A cylinder of radius R and height h is placed in uniform electric field as shown in Fig a if the axis of the cylinder made inclined with vertical as shown in Fig b Calculate the flux of electric field entering the cylinder 15 H 0 193

nr 3 A sphere of radius R has charge density given by P Po 1 3R where po is a constant r is distance from centre of sphere For a spherical gaussian surface of radius R centered at the centre of sphere the flux is zero Find n

47 An infinite uniformly charged sheet with surface charge density o cuts through a spherical Gaussian surface of radius R at a distance x from its center as shown in the figure The electric flux through the Gaussian surface is A R Q X solgreint solscenei baigns iden pionove boonlq ons p bre 11 1 02 000 aat of loups os ploilmugitmos orl to TR B G 2n R x o T R x o R x o