Suppose a Gaussian surface does not have any net charge inside it. Does it mean that the electric intensity E → is necessarily zero at all points on the surface? Is the converse true?

When net charge enclosed by the surface is zero (i.e., q = 0 ), then according to Gauss's theorem, electric flux = ϕ = ∮ E → · d A → = q ε 0 = 0 . . . ( 1 ) And according to measurement of electric flux ϕ = ∮ E → · d A → = E ∮ d A cos θ = E · ∮ d A cos θ . . . ( 2 ) From 1 and 2 , we get E · ∮ d A cos θ = 0 ⇒ E = 0 But when we consider E → as non-zero but A → is perpendicular to E → , then ϕ = ∮ E → · d A → = 0 and converse is also true. i.e., If E → is zero at every point on Gaussian surface, then flux = ∮ E → · d A → = 0 .

A cylinder is immersed in a uniform electric field E → with its axis parallel to the field. Show that the electric flux through the cylinder is zero.

According to given figure net electric flux through the cylinder immerged in electric field E → = ϕ n e t = ∮ E → · d A → Left face + ∮ E → · d A → Right face + ∮ E → · d A → Curved face But angle between E → and d A → in left face right face & curved face are 180 ° , 0 ° and 90 ° respectively. ∴ ϕ n e t = ∮ E d A cos 180 ° + ∮ E d A cos 0 ° + ∮ E d A cos 90 ° = - E ∮ d A + E ∮ d A + 0 = 0

E M B I B E

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 3

EASY

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IMPORTANT

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A point-charge is placed at the centre of a closed Gaussian spherical surface. How is electric flux $Φ_{E}$ , through the surface affected when

$(i)$ The sphere is replaced by a cylinder of the different volume?

Important Questions on Gauss' Theorem

EASY

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 3

A point-charge is placed at the centre of a closed Gaussian spherical surface. How is electric flux $Φ_{E}$ , through the surface affected when

(ii) The charge is shifted from the centre to some other place inside the sphere?

EASY

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 3

A point-charge is placed at the centre of a closed Gaussian spherical surface. How is electric flux $Φ_{E}$ , through the surface affected when

(iii) A second charge is placed inside the sphere?

EASY

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 3

A point-charge is placed at the centre of a closed Gaussian spherical surface. How is electric flux $Φ_{E}$ , through the surface affected when

(iv) The charge is replaced by an electric dipole?

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 4

Suppose a Gaussian surface does not have any net charge inside it. Does it mean that the electric intensity $\vec{E}$ is necessarily zero at all points on the surface? Is the converse true?

MEDIUM

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NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 5

State Gauss’ theorem. Draw a graph showing the variation of electric field, as one moves from the centre of a charged metal ball to a point on its surface and then to a far-off outside point.

HARD

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IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 2 - Gauss' Theorem>QUESTIONS>Q 6

A cylinder is immersed in a uniform electric field