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The total charge on a system is the algebraic sum of all individual charges in the system.

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

The radius of a nucleus is given by

r_{0} A^{1 / 3}

where

r_{0} = 1.3 \times 10^{- 15} m

and

A

is the mass number of the nucleus, the Lead nucleus has

A = 206

, the electrostatic force between two protons in this nucleus is approximately

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

A point charge

+ Q

is held at rest at a point

P .

Another point charge

- q

, whose mass is

m

, moves at a constant speed

v

in a circular orbit of radius

R_{1}

around

P

. The work required to increase the radius of revolution of

- q

from

R_{1}

, to another orbit

R_{2}

(R_{2} > R_{1})

(where K = \frac{1}{4 π ε_{0}})

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Four identical pendulums are made by attaching a small ball of mass

100 g

on a

20 cm

long thread and suspended from the same point. Now each ball is given charge

q

so that balls move away from each other with each thread making an angle of

45^{o}

from the vertical. The value of

q

is close to

(\frac{1}{4 {πε}_{0}} = 9 \times 10^{9}, S . I . u n i t s)

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two point charges A and B, having charges

+ Q

and

- Q

respectively, are placed at certain distance apart and force acting between them is

F

. If

25 %

charge of

A

is transferred to

B

, then the force between the charges becomes

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

The charge present in a doubly ionized helium atom is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Suppose the charge of a proton and an electron differ slightly. One of them is

e

, the other is

(e + Δ e)

. If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distance

d

(much greater than atomic size) apart is zero, then

Δ e

is of the order of [Given mass of hydrogen

m_{h} = 1.67 \times 10^{- 27} kg

]

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

The dimensions of

ε_{0}

(permittivity in free space) is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two electrons are moving with equal speed of

5 \times 10^{5} m s^{- 1}

parallel to each other. The ratio of the electrostatic to the magnetic force between them is

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two identical charged spheres suspended from a common point by two massless strings of lengths

l

, are initially at a distance

d (d ≪ l)

apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity

υ

. Then

υ

varies as a function of the distance

x

between the spheres, as

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two charges, each equal to

q

, are kept at

x = - a

and

x = a

on the x-axis. A particle of mass

m

and charge

q_{0} = - \frac{q}{2}

is placed at the origin. If charge

q_{0}

is given a small displacement

(y ≪ a)

along the y-axis, the net force acting on the particle is proportional to :

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

A certain charge

2 Q

is divided at first into two parts

q_{1}

and

q_{2}

. Later the charges are placed at a certain distance. If the force of interaction between two charges is maximum then

\frac{Q}{q_{1}} =

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Name two basic properties of electric charge.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is

α

. The spheres are now immersed in a dielectric liquid of density

800 kg m^{- 3}

and dielectric constant

21

. If the angle between the strings remains the same after the immersion, then

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two small metal balls of different masses

m_{1}

and

m_{2}

are connected by strings of equal length to a fixed point. When the balls are given equal charges, the angles that the two strings make with the vertical are

30 °

and

60 °

, respectively. The ratio

\frac{m_{1}}{m_{2}}

is close to,

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are

1.6 Å

apart is,

(m_{e} ≃ 9 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C)

(Take

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

)

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Three Point charges each equal to

+ q

are placed at the vertices of an equilateral triangle of side

' l'

. The net force on a charge

q_{1}

placed at the centre of the triangle is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two small metal spheres

A

and

B

charged positively are separated by

2 m

in air. The force on a charge of

+ 1 C

placed on the line joining the centres of the spheres and at a distance of

0.5 m

from

A

is found to be zero. The ratio

q_{A} : q_{B}

of charges on

A

and

B

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

Two positively charged spheres of masses

m_{1} and m_{2}

are suspended from a common point at the ceiling by identical insulating massless strings of length

l

. Charges on the two spheres are

q_{1} and q_{2}

, respectively. At equilibrium, both strings make the same angle

θ

with the vertical. Then

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

If a body gives out

10^{9}

electrons every second, how much time is required to get a total charge of

1 C

from it ?

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Charge and Its Basic Properties

The number of electrons in one

coulomb

charge is

The total charge on a system is the algebraic sum of all individual charges in the system.

Important Questions on Electrostatics

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