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

Let A cylinder of length l and radius r is placed in uniform electric field E → , with its axis parallel to field. Electric flux generated through cylindrical surface is three types. Let flux ϕ 1 is coming out from left circular area, flux ϕ 2 is coming out from right circular area and ϕ 3 will come from curved surface area. Now ϕ 1 + ϕ 2 = 0 , both are in opposite direction. So they are cancel out to each other. ϕ 3 = E . d a ⇒ ϕ 3 = E d a cos θ , Here electric field and curved surface are perpendicular to each other. So θ = 90 o , ∴ cos 90 = 0 ∴ ϕ 3 = 0 . Hence, the electric flux through the cylinder is zero.

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 6

MEDIUM

12th West Bengal Board

IMPORTANT

Earn 100

State Gauss's theorem in electrostatics. Using this theorem, prove that no electric field exists inside a hollow charged conducting sphere.

Important Questions on Gauss' Law and its Application

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 11

Explain why a soap bubble expands in volume when given a charge.

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12th West Bengal Board

IMPORTANT

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

Explain why charges accumulate more at sharp points of a conductor.

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12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 16

Is electric flux a scalar or a vector?

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 (i) infinitely long straight charged wire

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 3

Using Gauss's law show that any excess charge given to an isolated conductor resides entirely on the outer surface of the conductor. Show further that the same holds even if there is a cavity cut in the conductor.

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 7

A cylinder is placed in uniform electric field