EASY

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A charge of $4 μC$ is to be divided into two. The distance between the two divided charges is constant. Calculate the magnitude of the divided charges so that the force between them is maximum.

Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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>Coulomb's Law

Two charges of equal magnitudes and at a distance $r$ exert a force $F$ on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

The dimensional formula of coefficient of permittivity for free space (

ε_{0}

) in the equation

F = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}},

where symbols have their usual meanings, is

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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>Coulomb's Law

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>Coulomb's Law

Two equally charged metal spheres

A

and

B

repel each other with a force of

4 \times 10^{- 5} N

. Another identical uncharged sphere

C

is touched to

A

and then placed at the mid point of the line joining the spheres

A

and

B

. The net electric force on the sphere

C

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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>Coulomb's Law

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>Coulomb's Law

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 :

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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}} =

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

Three identical charges each of magnitude

3 μ C

are placed at the corners of a right angled triangle

ABC

whose base

B C

and height

B A

are

3 cm

and

4 cm

respectively. Forces on the charge at right angled corner

B

due to charges at

A

and

C

are

F_{1}

and

F_{2}

respectively. The angle between their resultant force and

F_{2}

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

The force of repulsion between two identical positive charges when kept, with a separation '

r

' in the air is '

F

'. Half the gap between the two charges is filled by a dielectric slab of dielectric constant

= 4

. Then, the new force of repulsion between those two charges becomes

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance $2 d$ . If the negative charge is given a small displacement $x (x ≪ d)$ perpendicular to the line joining the positive charges, how the force $(F)$ developed on it will approximately depend on $x$ ?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

Let $[\in_{0}]$ denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

HARD

Physics>Electricity and Magnetism>Electrostatics>Coulomb's Law

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

A charge of 4 μC is to be divided into two. The distance between the two divided charges is constant. Calculate the magnitude of the divided charges so that the force between them is maximum.

Important Questions on Electrostatics

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A charge of $4 μC$ is to be divided into two. The distance between the two divided charges is constant. Calculate the magnitude of the divided charges so that the force between them is maximum.