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

HARD

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Initially two charged particles $A$ and $B$ are moving with same velocity along $x -$ axis when uniform electric field is applied in that region. Velocity of $A$ changes its direction by $60 °$ and speed is doubled direction of $B$ changes by $30 °$ then ratio of specific charges

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Important Questions on Electric Charges and Fields

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

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field

\vec{E}

. Due to the force

q \vec{E}

, its velocity increases from 0 to

6 m s^{- 1}

in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between

0

3

seconds are respectively

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)

EASY

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

Charges $Q_{1}$ and $Q_{2}$ are at points $A$ and $B$ of a right-angled triangle $O A B$ . The resultant electric field at point $O$ is perpendicular to the hypotenuse, then $Q_{1} / Q_{2}$ is proportional to:

Question Image

MEDIUM

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

An electric field due to a positively charged long straight wire at a distance

r

from it is proportional to

r^{- 1}

in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii

1 \overset{\circ}{A}

and

2 \overset{\circ}{A}

. The ratio of their respective time periods is

HARD

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

A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V_{0}$ . When it passes through the origin it enters a region having uniform electric field $\vec{E} = - E \hat{j}$ which extends upto $x = d$ . Equation of path of electron in the region $x > d$ is:

Question Image

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

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 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})

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

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})

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}]

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 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

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)

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})

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 particle, of mass

10^{- 3} kg

and charge

1.0 C

, is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

\vec{E} (t) = E_{0} \sin (ω t) \hat{i}

, where

E_{0} = 1.0 N C^{- 1}

and

ω = 10^{3} rad s^{- 1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in

m s^{- 1}

, attained by the particle at subsequent times is ____________.

HARD

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

An electron falls from rest through a vertical distance

h

in a uniform and vertically upward directed electric field

E

. The direction of electric filed is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance

h

. The time of fall of the electron, in comparison to the time of fall of the proton is

Initially two charged particles A and B are moving with same velocity along x- axis when uniform electric field is applied in that region. Velocity of A changes its direction by 60° and speed is doubled direction of B changes by 30° then ratio of specific charges

Important Questions on Electric Charges and Fields

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Initially two charged particles $A$ and $B$ are moving with same velocity along $x -$ axis when uniform electric field is applied in that region. Velocity of $A$ changes its direction by $60 °$ and speed is doubled direction of $B$ changes by $30 °$ then ratio of specific charges