Introduction

An Electric Charge at rest creates an Electrostatic Field. A moving electric charge creates Electric as well as Magnetic Field. And an accelerating charge creates ElectroMagnetic Radiation. But aren?t velocity and acceleration, relative terms ?

Electric Charge - 1

Can we really define what is an electric charge ? Overview and History of an ?electric charge?. Categorization of Positive and Negative charges.

Electric Charge - 2

Categorization of Conductors and Insulators. Electric Induction. Charging by Induction and Charging by Conduction. Principle of Conservation of Charge. Quantization of Charge.

Q1

Statement - 1
Two identical metal spheres A and B of exactly equal masses are taken. Sphere A is given a positive charge and sphere B an equal negative charge. After charging, the mass of A will be less than that of B.

Statement - 2
A charging process involves a transfer of electrons.

Q2

A glass rod acquires a charge of when rubbed with a silk cloth.
a) Find the number of electrons lost by glass rod.
b) Find the negative charge acquired by silk.
c) Is there transfer of mass from glass to silk ?

Q3

It is given that objects A and B attract each other and objects B and C attract each other. For the two cases where,
i) A, B and C are point charges
ii) A, B and C are extended bodies (not point charges)
Find,
If A and C held closed together they will
a. attract
b. repel.
c. not attract each other
d. more information is needed to answer

Gold Leaf Electroscope

Working of the Gold Leaf Electroscope used to detect the polarity of electric charge.

Millikan\'\'s Oil Drop Exp

Working of Millikans Oil Drop Experiment used to determine the quantized nature of electric charge which led to the discovery of electron.

Coulomb\'\'s Law

Coulombs Law

Q4

If you were able to isolate two identical charged particles of mass m from all external forces,
(a)For what value of charge and mass can the two particles remain in equilibrium ? Comment on the nature of equilibrium.
(b)What is the minimum value of m so that they can be held in such a configuration?

Q5

Figure shows four situations in which particles of charge +q or ?q are fixed in plane. In each, the particles on the -axis are equidistant from the y-axis. The particle on the y-axis experiences an electrostatics force F from each of these two particles.
a) are the magnitudes F of those forces the same or different ?
b) do the x components of the two forces add or cancel ?
c) do the y components of the forces add or cancel ?
d) is the direction of the net force on the middle particle that of the canceling components or the adding components ?
e) is the magnitude of the net force on the particle on the y-axis equal to, greater than or less than 2F ?

Q6

Find the net force acting on the center charge in the two cases shown below.

Electric Field

Concept of Electric Field and Field Lines. Does a charge affect the electric field of another charge ?

Q7

Three negative point charges -q each, and three positive point charges +q, +q and +Q are placed at the vertices of a regular hexagon as shown in the figure. For what value of Q will the electric field at O to due to the five charges at A, B, D, E and F be twice the electric field at centre O due to charges Q at C alone?

Q8

Can the electric field due to two charges ever vanish except along a line connecting the two charges?
If we are given that the electric field at some point beyond the region between two point charges vanishes.
(a) What are the signs of the charges?
(b) Can these charges be equal in magnitude?

Q9

Assuming only electrostatic force are present, electric field lines in the space surrounding a charge distribution show
a) Only the directions in which static charges would accelerate when at points on those lines.
b) Only the direction in which moving charges would accelerate when at points on those lines.
c) Tangents to the direction in which either static or moving charge would accelerate when passing through points on those lines.
d) The paths static or moving charges would take.

Field - Ring

Electric Field on the axis of a Uniformly charged Ring. Will the field be different for a Non-Uniformly charged ring ?

Q10

In the figures shown below, find the ratio of charge on rings so that the net field at point P is zero.

Field due to Arc

Electric Field at the center of a Uniformly charged Arc. Difference between Re-Distribution of Charge ( Q is constant ) and Addition of Segments ( Charge Density is constant )

Q11

Rank the given arrangement according to the magnitude of the electric field at the center of curvature.

Field - Shell

Electric Field due to a Uniformly charged Shell. Why is the Field inside a uniformly charged shell zero ?

Field - Sphere

Electric Field due to a Uniformly charged solid Sphere and ?Radially Non-Uniformly charged? solid Sphere.

Field - Disc

Electric Field on the axis of a Uniformly charged Disk.

Q12

At what distance along the central perpendicular axis of a uniformly charged plastic disk of radius R is the magnitude of the electric field equal to
a) one-half the magnitude of the field at the center of the surface of the disk ?
b) one-third the magnitude of the field at the center of the surface of the disk ?

Q13

Two discs have same surface charge density but different radius. If their fields at distance z1 and z2 are equal, find the ratio z1 / z2.

Field - Line

Electric Field due to a Uniformly charged Finite, Semi-Infinite and Infinite wire.

Field - Sheet

Electric Field due to a Uniformly charged Infinite Sheet.

Field - Dipole

Electric Field due to an Electric Dipole

Q16

Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Dipole in Field

Force and Torque on an Electric Dipole placed in an Electric Field.

Q17

Statement 1: If a water molecule is kept near an infinite uniform sheet of charge, it may rotate, but it will not move toward or away from the sheet.

Statement 2: The net force on a dipole in a uniform electric field is zero.

Q18

An electric dipole is placed near a positive charge. It will experience

(a) a torque only
(b) a force only
(c) both torque and force
(d) it will depend on the orientation of the dipole with respect to the charge.

2

Two identical charged balls are suspended by strings of equal length. The string make an angle q with the vertical. When suspended in a liquid of density r kg m-3, the angle remains the same. What is the dielectric constant of the liquid? The density of the material of the sphere is r kg m-3

In the initial situation, when the charges were not in liquid, would the angle be same or different if the charges were equal or different ?.

If the charges were different and are now equally distributed between the balls, would the angle between the strings increase, decrease, or stay the same?

5

An electron and a porton start moving parallel to the plates towards the other end from the midpoint of the separation of plates at one end of the plates. Which of the two will have greater deviation when they come out of the plates if they start with the
a) same initial velocity,
b) same initial kinetic energy and
c) same initial momentum.

6

A negatively charged particle is moving in the positive x direction when it enters a region with a uniform electric field pointing in the positive x direction. Which of the following graphs represents its position as a function of time ?
( Its initial position is x = 0 at t = 0 )

7

A region in space contains a uniform electric field of Ex = 0 and Ey V/m and no gravitational field. A particle of mass m kg and charge -q C is moving to the right

with a speed of v m/s at t = 0.

(a) Find the acceleration of particle.
(b) Find the x position of particle at t sec.
(c) Find the y position of particle at t sec.

8

A particle of charge Q is fixed at the origin of an x-y coordinate system. At t = 0 a particle of mass m kg and magnitude of charge q C, is located at x = r meters,
moving with a speed of v m/s in the positive y direction.

For what value of Q will the moving particle execute circular motion ?
What will be the time period ?
( Neglect the gravitational force between the particles)

9

A uniform upward electric field E of magnitude 1.76 ? 103 N/C has been set up between two horizontal plates. The plates have length L = 5 cm and separation d = 1.5 cm. An electron is shot between the plates from the left edge of the lower plate. The initial velocity of the electron has a magnitude of 2 ? 1.76 m/s and makes an angle q = 45o with the lower plate.

Will the electron strike one of the plates?

( electrons charge to mass ratio is = 1.76 ? 1011 C/kg )

10

Two point charges having the same magnitude but opposite signs are placed at a separation of l. E is plotted against x for values of x from close to zero to slightly less than l. Which of the following best represents the resulting graph ?

11

Two point-like charges whose magnitudes are equal are positioned at a certain distance from each other. Determine the sign of charges for each graph of the field strength between charges.

12

For the two system of charges shown in figure,
a) Plot the variation of E along x-axis.
b) Plot the variation of E along y-axis.

13

For the given system of charges, which of the following graphs best represents the electric field on x axis ?

14

Three non-conducting infinite planes of A, B and C are vertical and parallel to one another. There is a uniform electric field E to the left of plane A and a uniform electric field to the right of plane C, The field E points to the left and the field E points to the right. The signs of the charges on plates A, B and C may be
a) -, -, -
b) +, -, -
c) +, -, +
d) +, +, +

15

Three non conducting infinite planer sheet are parallel to the y - z plane. Each sheet has a uniform surface charge density. The first sheet, with a negative surface charge density - , passes through the x axis at x = 3 m. The second sheet has an unknown surface charge density and passes through the x axis at x = 4m. The third sheet has a negative surface charge density - 3 and passes through the x axis at x = 6 m. The net electric field due to the sheet is zero at x = 3.5 m.
a) What is the surface charge density on the second sheet ?
b) If the electric field at x = 0 is Eo, what is the electric field at (i) x = -10 m (ii) x = 5 m (iii) x = 8 m

17

Find the force on a small electric dipole of dipole moment p due to a point charge Q placed at a distance r, for the two configurations shown below

18

Consider a point P whose position vector makes an angle q with the dipole moment. What is the angle made by the electric field at a point P with the dipole moment ?

For what value(s) of angle q is the electric field due to dipole perpendicular to the dipole moment.

19

Two point particles of mass m are attached to the ends of a mass less rigid non-conducting rod of length d. The two particles carry charges +q and ?q. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle q with the field direction as shown in the figure

20

Under the influence of the coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s).

a) angular momentum of the charge -q is constant
b) linear momentum of the charge -q is constant
c) angular velocity of the charge -q is constant
d) linear speed of the charge -q is constant

21

Two equal negative charges -q are fixed at points ( 0, a ) and ( 0, - a ). A positive charge +Q is released from rest at the point ( a, 0 ) on the x axis, The charge Q will
(a) execute SHM about the origin.
(b) move to the origin and remain at rest there.
(c) move to infinity.
(d) execute oscillations but not SHM.

24

Three charges -q, +2q and -q are arranged on a line. Calculate the field at a distance r on the line as shown (assume r >> d )

25

A semi-infinite-charged rod is placed such that its one end coincides with the center of a charged ring as shown in fig. Both of them have a charge per unit length of l. The radius of ring is R, its cross sectional area is A and Youngs modulus is Y. What is the
a) force on rod due to ring ?
b) force on ring due to rod ?
c) increase in Tension in Ring ?
d) increase in radius of ring ?

26

Two mutually perpendicular infinite straight lines of charge with uniform linear charge densities l1 and l2 are positioned at a distance a from each other.
What is the force between the lines ? Does force depends on a ?

27

Two balls of charges q1 and q2 are initially moving with the same speed and in same direction. After a uniform electric field has been applied for a certain time interval, the direction of first ball changes by 60o and the speed is reduced to half. The direction of velocity of the second ball changes by 90o.
Determine the magnitude of the charge-to-mass ratio of the second ball if it is equal to a1 for the first ball.
In what ratio will the velocity of the second ball change ?

28

A rigid insulated wire frame in the form of a right-angled triangle ABC, is set in a vertical plane as shown in the figure. Two beads of equal masses m and carrying charges q1 and q2 are connected by a chord of length l and can slide without friction on the wires. The beads are stationary.
i) The value of angle a is
ii) The tension in the chord is
iii) The normal reaction on bead P is
iv) The normal reaction of bead Q is
v) If the chord is cut, the magnitude of the product | q1 q2 | of the charges for which the beads continue to remain stationary is

29

Find the field due to a uniformly charged arc (making an angle 2a at its centre), at a point lying at a distance z from its centre as shown in figure.

30

Two similar balls, each of mass m and charge q, are hung from a common point by two threads, each of length l. Show that separation between the ball is
Find the rate dq/dt with which the charge should leak off each sphere if the velocity of approach varies as v = a / rout2 where a is a constant

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