Find the electric flux through the surface in the following cases: An uniform electric field of intensity 6 × 10 3 N / C is directed along, X -axis. The length and breadth of a rectangular plane surface is 1 m and 0 . 5 m respectively. (ii) When the surface is parallel to X Y -plane.

Given, E l e c t r i c f i e l d o f d e n s i t y E = 6 × 10 3 N / C L e n g t h o f a r e c tan g u l a r p l a n e s u r f a c e l = 1 m B r e a d t h o f a r e c tan g u l a r p l a n e s u r f a c e b = 0 . 5 m θ = 60 ∘ Area of rectangular plane surface, A = l × b = 1 × 0 . 5 Therefore, electric flux is given by, ϕ = E A cos θ = 6 × 10 3 × 1 × 0 . 5 × cos 60 ∘ ⇒ ϕ = 3 × 10 3 × 1 2 = 1 . 5 × 10 3 N m 2 C - 1

A spherical Gaussian surface encloses a charge of 8 . 85 × 10 - 8 C . Calculate the electric flux passing through the surface?

Given, that the net charge inside the surface Q = 8.85 × 10 - 8 C From the Gauss law, net flux through the surface ϕ E = Q ε 0 = 8.85 × 10 - 8 C 8.85 × 10 - 12 C 2 N - 1 m - 2 = 10 4 N m 2 C - 1 . The electric flux passing through the surface is = 10 4 Nm 2 C - 1 . Hence, it is the required answer

A spherical Gaussian surface encloses a charge of 8 . 85 × 10 - 8 C (ii) If the radius of the Gaussian surface is doubled, how would the flux change?

The flux does not depend upon the size of the Gaussian surface but only on the charges enclosed. So, in this case also Φ = 10 4 Nm 2 /C.

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12th West Bengal Board

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Calculate the electric potential due to a uniformly charged rod at a point on its perpendicular bisector.

Important Questions on Gauss' Law and its Application

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 15

Calculate the electrical potential energy of a uniformly charged sphere.

MEDIUM

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

An uniform electric field of intensity

6 \times 10^{3} N / C

is directed along,

X

-axis. The length and breadth of a rectangular plane surface is

1 m

and

0.5 m

respectively. Find the electric flux through the surface in the following cases:

(1) when the surface is parallel to $Y Z$ -plane.

MEDIUM

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

Find the electric flux through the surface in the following cases:

An uniform electric field of intensity $6 \times 10^{3} N / C$ is directed along, $X$ -axis. The length and breadth of a rectangular plane surface is $1 m$ and $0.5 m$ respectively.

(ii) When the surface is parallel to $X Y$ -plane.

MEDIUM

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

An uniform electric field of intensity

6 \times 10^{3} N / C

is directed along,

X

-axis. The length and breadth of a rectangular plane surface is

1 m

and

0.5 m

respectively. Find the electric flux through the surface in the following cases:

(c) the length of the surface is parallel to $Y$ -axis, but the normal drawn to it is inclined to the $X$ -axis at an angle of $60^{°}$ .

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

A small metal sphere carrying charge $+ Q$ is located at the centre of a spherical cavity in a large uncharged metal sphere as shown in the figure, Fig. $3.72$ . Use Gauss's law to find electric field at points $P_{1}$ and $P_{2}$ .

Question Image

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 5

A spherical Gaussian surface encloses a charge of

8.85 \times 10^{- 8} C

. Calculate the electric flux passing through the surface?

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 5

A spherical Gaussian surface encloses a charge of

8.85 \times 10^{- 8} C

(ii) If the radius of the Gaussian surface is doubled, how would the flux change?

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 3 - Gauss' Law and its Application>EXERCISE 3>Q 6

A charge of

17.7 \times 10^{- 4} C

is distributed uniformly over a large sheet of area

200 m^{2}

. Calculate the electric field intensity at a distance

20 cm

from it in air.

Calculate the electric potential due to a uniformly charged rod at a point on its perpendicular bisector.

Important Questions on Gauss' Law and its Application

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