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

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 ^

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The magnitude of point charge due to which the electric field 30 cm away from it has the magnitude $2 N- C^{- 1}$ will be

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Important Questions on Electric Charges and Fields

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>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})

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

Suppose that intensity of a laser is

(\frac{315}{π}) W m^{- 2} .

The rms electric field, in units of

V m^{- 1}

associated with this source is close to the nearest integer is

- (ε_{0} = 8.86 \times 10^{- 12} C^{2} N m^{- 2}; c = 3 \times 10^{8} m s^{- 1})

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>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)

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>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:

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

Two identical charged spheres separated by a distance repel each other with a force

F

. If

10 %

of electrons are transferred from one sphere to the other than the force between them becomes

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>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)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

A point charge of

50 μ C

is placed in the

X Y

plane at a location with radius vector

{\vec{r}}_{0} = 2 \hat{i} + 3 \hat{j} m

The electric field strength and its magnitude at a point with radius vector

\vec{r} = 8 \hat{i} - 5 \hat{j} m

(ε_{o} = 8.85 \times 10^{- 12} C^{2} N - m^{- 2})

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>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>Electric Charges and Fields>Electric Field

An infinite line of charge with uniform line charge density of

1 C m^{- 1}

is placed along the

y

-axis. A charge of

1 C

is placed on the

x

-axis at a distance of

d = 3 m

from the origin. At what distance

(r)

from the origin on the

x

-axis, the total electric field is zero.

N

(Assume

0 < r < d

)

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

There is a uniform electric field of strength

10^{3} V m^{- 1}

along the

Y -

axis. A particle of mass

1 g

and charge

10^{- 6} C

is projected into the field from the origin along the

+ ve X

-axis with a velocity of

40 m s^{- 1}

. Then the magnitude of its velocity after

30 seconds

will be (neglect gravitation)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

An electrostatic field line leaves at an angle

α

from point charge

q_{1}

and connects with point charge

- q_{2}

at an angle

β

(

q_{1}

and

q_{2}

are positive) see figure below. If

q_{2} = \frac{3}{2} q_{1}

and

α = 30 °,

then

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Field

Two masses

M_{1}

and

M_{2}

carry positive charges

Q_{1}

and

Q_{2},

respectively. They are dropped to the floor in a laboratory set up from the same height, where there is a constant electric field vertically upwards.

M_{1}

hits the floor before

M_{2}

. Then,

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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>Electric Charges and Fields>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:

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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}]

The magnitude of point charge due to which the electric field 30 cm away from it has the magnitude 2 N-C-1 will be

Important Questions on Electric Charges and Fields

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The magnitude of point charge due to which the electric field 30 cm away from it has the magnitude $2 N- C^{- 1}$ will be