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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Figure shows a metal ball of mass $50 kg$ and radius $\frac{2}{\sqrt{π}} m$ is placed on an insulating uncharged stand. In space an upward uniform electric field $5 \times 10^{5} N C^{- 1}$ is switched on. A stream of light ions is incident on the ball from left side at a speed $2 \times 10^{6} m s^{- 1}$ as shown in figure. If charge on ball at $t = 0$ was zero and incidence starts at this moment, find the time in seconds at which ball will be lifted from the stand. The charge density of ion beam is $5 \times 10^{- 12} C m^{- 3}$ . Assume that all charge incident on the ball is absorbed. (Take $g = 10 m s^{- 2}$ )

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Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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:

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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:

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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:
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HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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>Electrostatics>Electric Field and Potential

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

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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

)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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})

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field and Potential

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
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