The electric fields of two plane electromagnetic plane waves in vacuum are given by E 1 → = E 0 cos ω t - k x j ^ and E 2 → = E 0 cos ω t - k y k ^ , at t = 0 , a particle of charge q is at origin with a velocity v → = 08 c j ^ ( c is the speed of light in vaccum). The instantaneous force experienced by the particle is:

E 0 q 0 .8 i ^ + j ^ + 0 .2 k ^

E 0 q 0 .8 i ^ - j ^ + 0 .4 k ^

E 0 q 0 .4 i ^ - 3 j ^ + 0 .8 k ^

A uniform electric field, E → = - 400 3 j ^ N C - 1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2 10 × 10 6 m s - 1 . This particle is aimed to hit a target T , which is 5 m away from its entry point into the field as shown schematically in the figure. Take q m = 10 10 C kg - 1 . Then

time taken by the particle to hit T could be 5 6 μ s as well as 5 2 μ s

the particle will hit T if projected at an angle 45 ° from the horizontal

time taken by the particle to hit T is 5 3 μ s

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An annular disc has inner and outer radius $a$ and $b$ . Surface density of charge is $σ$ . The electric field at any point at a distance $y$ along the axis of the disc is given by

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Important Questions on Interaction of Charged Particles, Electric Field and Potential

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A particle of mass

m

and charge

q

is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed

v

on the distance

x

travelled by it is correctly given by (graphs are schematic and not drawn to scale)

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

The bob of a simple pendulum has mass

2 g

and a charge of

5.0 μ C .

It is at rest in a uniform horizontal electric field of intensity

2000 V / m

At equilibrium, the angle that the pendulum makes with the vertical is:

(t a k e g = 10 m / s^{2})

MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A simple pendulum of length

L

is placed between the plates of a parallel plate capacitor having electric field

E

, as shown in figure. Its bob has mass

m

and charge

q

. The time period of the pendulum is given by:
Question Image

MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A particle of mass

m

and charge

q

is placed at rest in uniform electric field

E

and then released. The kinetic energy attained by the particle after moving a distance

y

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density

λ

are kept parallel to each other. In their resulting electric field, point charges

q

and

- q

are kept in equilibrium between them. The point charges are confined to move in the

x

direction only. If they are given a small displacement about their equilibrium positions, then the correct statements(s) is (are)

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MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

The electric fields of two plane electromagnetic plane waves in vacuum are given by

\vec{E_{1}} = E_{0} \cos (ω t - k x) \hat{j}

and

\vec{E_{2}} = E_{0} \cos (ω t - k y) \hat{k}

, at

t = 0,

a particle of charge

q

is at origin with a velocity

\vec{v} = 08 c \hat{j}

(

c

is the speed of light in vaccum). The instantaneous force experienced by the particle is:

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Four point charges

- q, + q, + q

and

- q

are placed on y-axis at

y = - 2 d, y = - d,

and

y = + 2 d,

respectively. The magnitude of the electric field

E

at a point on the x-axis at

x = D,

with

D ≫ d,

will behave as:

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

An infinitely long thin straight wire has uniform charge density of

\frac{1}{4} \times 10^{- 2} C m^{- 1}

. What is the magnitude of electric field at a distance

20 cm

from the axis of the wire?

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A wire of length

L = 20 c m

is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges

+ Q

and

- Q

as shown in the figure. The magnitude of the charge on each half is

|Q| = 10^{3} ε_{0}

, where

ε_{0}

is the permittivity of free the space. The net electric field at the centre

O

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

The electric field in a certain region is acting radially outward and is given by

E = A r

. A charge contained in a sphere of radius

a

centred at the origin of the field will be given by

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Two charged thin infinite plane sheets of uniform charge density

σ_{+}

and

σ_{-}

, where

|σ_{+}| > |σ_{-}|

, intersect at the right angle. Which of the following best represents the electric field lines for the system:

MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Two point charges

q_{1} (\sqrt{10} μC)

and

q_{2} (- 25 μC)

are placed on the

x

-axis at

x = 1 m

and

x = 4 m

respectively. The electric field

(in V m^{- 1})

at a point

y = 3 m

y

-axis is,

[Take \frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}]

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A spherical conductor of radius

10 cm

has a charge of

3.2 \times 10^{- 7} C

distributed uniformly. What is the magnitude of electric field at a point

15 cm

from the centre of the sphere?

(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} C^{- 2})

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Three charged particles $A, B$ and $C$ with charges $- 4 q, 2 q$ and $- 2 q$ are present on the circumference of a circle of radius $d .$ The charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in the figure. The electric field at the point $O$ is
Question Image

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Two metal plates having a potential difference of

800 V

are

2 cm

apart. It is found that a particle of mass

1.96 \times 10^{- 15} kg

remains suspended in the region between the plates. The charge on the particle must be (

e =

elementary charge)

EASY

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Four point charges $q_{A} = 2 μ C, q_{B} = - 5 μ C, q_{C} = 2 μ C, q_{D} = - 5 μ C$ are located at the corners of a square $A B C D$ of side $10 cm .$ The force acting on a charge of $1 μ C$ placed at centre of the square is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A particle of mass

2 \times 10^{- 6} kg

with a charge

5 \times 10^{- 6} C

is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume

ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} M^{- 2}

and

g = 10 m s^{- 2}

)

MEDIUM

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

Two parallel infinite line charges with linear charge densities

+ λ C m^{- 1}

and

- λ C m^{- 1}

are placed at a distance of

2 R

in free space. What is the electric field mid-way between the two-line charges?

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A thin disc of radius $b = 2 a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $σ$ on it. If the electric field on its axis at a height $h (h < < a)$ from its centre is given as $C h$ then the value of $C$ is

Question Image

HARD

Physics>Electricity and Magnetism>Interaction of Charged Particles, Electric Field and Potential>Electric Field

A uniform electric field, $\vec{E} = - 400 \sqrt{3} \hat{j} N C^{- 1}$ is applied in a region. A charged particle of mass $m$ carrying positive charge $q$ is projected in this region with an initial speed of $2 \sqrt{10} \times 10^{6} m s^{- 1}$ . This particle is aimed to hit a target $T$ , which is $5 m$ away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m} = 10^{10} C {kg}^{- 1}$ . Then

Question Image

An annular disc has inner and outer radius aand b. Surface density of charge is σ. The electric field at any point at a distance y along the axis of the disc is given by

Important Questions on Interaction of Charged Particles, Electric Field and Potential

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An annular disc has inner and outer radius $a$ and $b$ . Surface density of charge is $σ$ . The electric field at any point at a distance $y$ along the axis of the disc is given by