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Two positive charges $q_{1}$ and $q_{2}$ are located at the points with radius vectors $r_{1}$ and $r_{2}$ . Find a negative charge $q_{3}$ and a radius vector $r_{3}$ of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero.

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Important Questions on Electric Charges and Fields

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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}

)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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}} =

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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,

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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}

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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}})

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

The dimensions of

ε_{0}

(permittivity in free space) is

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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 $x$ ?

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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>Electric Charges and Fields>Coulomb's Laws

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

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Coulomb's Laws

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

Two positive charges q1 and q2 are located at the points with radius vectors r1and r2. Find a negative charge q3and a radius vector r3 of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero.

Important Questions on Electric Charges and Fields

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Two positive charges $q_{1}$ and $q_{2}$ are located at the points with radius vectors $r_{1}$ and $r_{2}$ . Find a negative charge $q_{3}$ and a radius vector $r_{3}$ of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero.