An infinite line charge produces a field of 9 × 10 4 NC - 1 at a distance of 4 cm . Calculate the linear charge density.

Given, The electric field produced by the infinite linear charge E = 9 × 10 4 N C - 1 Distance at which electric field is calculated d = 4 cm = 4 × 10 - 2 m Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d ⇒ λ = 2 π ε 0 E d = 4 π ε 0 E d 2 = 9 × 10 4 × 0 . 04 9 × 10 9 × 2 = 2 × 10 - 7 Cm - 1 Therefore, the linear charge density is 2 × 10 - 7 Cm - 1

A cylinder of large length carries a charge of 2 × 10 - 8 Cm - 1 . Find the electric field at a distance of 0 . 2 m from it.

Given, Linear charge density of the cylinder λ = 2 × 10 - 8 Cm - 1 Distance at which electric field is calculated d = 0 . 2 m Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d = 1 4 π ε 0 · 2 λ d = 9 × 10 9 × 2 × 2 × 10 - 8 0 . 2 = 4 . 495 × 10 19 NC - 1 m - 1

An electron is revolving around a long line charge having charge density 2 × 10 − 8 C m − 1 . Find the kinetic energy of the electron, assuming that it is independent of the radius of electron's orbit.

Linear charge density of the line charge λ = 2 × 10 − 8 C m − 1 Electric field due to infinite linear charge at a distance d from it is E = λ 2 π ε 0 d Force acting on the electron revolving, m v 2 d = E e = λ e 2 π ε 0 d ⇒ 1 2 m v 2 = λ e 4 π ε 0 ⇒ Kinetic energy K = λ e 4 π ε 0 = 9 × 10 9 × 2 .0 × 10 − 8 × 1 .6 × 10 − 19 = 2 .88 × 10 − 17 J

EASY

12th CBSE

IMPORTANT

Earn 100

The electric field components due to a charge inside the cube of side $0.1 m$ are as shown.

$E_{x} = α x$ , where $α = 100 N / C^{- m}$

$E_{y} = 0, E_{z} = 0$

Calculate (i) the flux through the cube, and (ii) the charge inside the cube.

Important Questions on Electric Charges and Field

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 11

A uniform electric field

\vec{E} = E_{x} \hat{i} N / C

for

x > 0

and

\vec{E} = - E_{x} \hat{i} N / C

for

x < 0

are given. A right circular cylinder of length

l cm

and radius

r cm

has its centre at the origin and its axis along the x-axis. Find out the net outward flux. Using Gauss's law write the expression for the net charge within the cylinder.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 1

An infinite line charge produces a field of

9 \times 10^{4} {NC}^{- 1}

at a distance of

4 cm

. Calculate the linear charge density.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 2

A cylinder of large length carries a charge of

2 \times 10^{- 8} {Cm}^{- 1}

. Find the electric field at a distance of

0.2 m

from it.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 3

An infinitely long wire is stretched horizontally

4

metre above the surface of the earth. It carries a charge

1 μC

per cm of its length. Calculate its electric field at a point on the earth's surface vertically below the wire.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 4

Two large metal plates each of area

1 m^{2}

are placed facing each other at a distance of

10 cm

and carry equal and opposite charges on their faces. If the electric field between the plates is

100 {NC}^{- 1}

, find the charge on each plate.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 5

An electron is revolving around a long line charge having charge density

2 \times 10^{- 8} C m^{- 1}

. Find the kinetic energy of the electron, assuming that it is independent of the radius of electron's orbit.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 6

A particle of mass

5 \times 10^{- 6} g

is kept over a large horizontal sheet of charge density

4 \times 10^{- 6} {Cm}^{- 2}

. What charge should be given to this particle, so that if released, it does not fall down. How many electrons should be removed to give this charge?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 7

A spherical shell of metal has a radius of

0.25 m

and carries a charge of

0.2 μC

. Calculate the electric field intensity at a point (i) inside the shell, (ii) just outside the shell and (iii)

3.0 m

from the centre of the shell.

The electric field components due to a charge inside the cube of side 0.1 m are as shown. Ex=αx, where α=100 N/C−m Ey=0, Ez=0 Calculate (i) the flux through the cube, and (ii) the charge inside the cube.

Important Questions on Electric Charges and Field

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The electric field components due to a charge inside the cube of side $0.1 m$ are as shown.

$E_{x} = α x$ , where $α = 100 N / C^{- m}$

$E_{y} = 0, E_{z} = 0$

Calculate (i) the flux through the cube, and (ii) the charge inside the cube.