The
electrostatic force on a small sphere of charge due to another
small sphere of charge in air is 0.2 N. (a)
What is the distance between the two spheres? (b)
What is the force on the second sphere due to the first?
(a) Explain the meaning of the statement, ‘electric charge of a body is quantised.’
(b) Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?
When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.
Four
point charges or and are located at the
corners of a square ABCD of side 10 cm. What the force on a charge is of placed at the
centre of the Square?
(a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
(b) Explain why two field lines never cross each other at any point?
Two
point charges and are located 20 cm
apart in vacuum. (a)
What is the electric field at the midpoint O of the line AB joining the two
charges? (b)
If a negative test charge of magnitude is placed at this
point, what is the force experienced by the test charge?
A
system has two charges and
located at points A
: (0, 0, ?15 cm) and B : (0, 0, + 15 cm) respectively. What are the total
charge and electric dipole moment of the system?
An
electric dipole with dipole moment is aligned at with the direction
of a uniform electric field of magnitude . Calculate the
magnitude of the torque acting on the dipole.
A polythene piece rubbed with wool is found to have a negative
charge of . (a) Estimate the number of electrons transferred
(from which to which?) (b) Is there a transfer of mass from wool to
polythene?
(a)
Two insulated charged copper spheres A and B have their centres separated by a
distance of 50 cm. What is the mutual force of electrostatic repulsion if the
charge on each is ? The radii of A
and B are negligible compared to the distance of separation. (b)
What is the force of repulsion if each sphere is charged double the above
amount, and the distance between them halved?
Suppose the spheres A and B in Q.1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B?
Figure
shows tracks of three charged particles in a uniform electrostatic field. Give
the signs of the three charges. Which particle has the highest charge to mass
ratio?
Consider
a uniform electric field.
(a)
What is the flux of this field through a square of 10 cm on a side whose plane
is parallel to the yz plane? (b)
What is the flux through the same square if the normal to its plane makes aangle with the
x-axis?
What is the net flux of the uniform electric field of Problem 1.15 through a cube of side 20 cm oriented so that its faces are parallel to the co-ordinate planes?
Careful
measurement of the electric field at the surface of a black box indicates that
the net outward flux through the surface of the box is .
(a)
What is the net charge inside the box? (b)
If the net outward flux through the surface of the box were zero, could you
conclude that there were no charges inside the box? Why or why not?
A
point charge is a distance 5 cm
directly above the centre of a square of side 10 cm, as shown in the given
figure. What is the magnitude of the electric flux through the square? Hint: Think of the
square as one fact of a cube with edge 10 cm.
A point charge causes an electric flux of to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
A
conducting sphere of radius 10 cm has an unknown charge. If the electric field
20 cm from the centre of the sphere is and points radially
inward, what is the net charge on the sphere?
A
uniformly charged conducting sphere of 2.4 m diameter has a surface charge
density of .
(a)
Find the charge on the sphere. (b)
What is the total electric flux leaving the surface of the sphere?
Two
large, thin metal plates are parallel and close to each other. On their inner
faces, the plates have surface charge densities of opposite signs and of
magnitude. What is E : (a)
in the outer region of the first plate, (b)
in the outer region of the second plate, and (c)
between the plates ?
An
oil drop of 12 excess electrons is held stationary under a constant electric
field of in Millikan's oil
drop experiment. The density of the oil is . Estimate the
radius of the drop.
In a certain region of space, electric field is alongthez-direction
throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of per
metre. What are the force and torque experienced by a system having
a total dipole moment equal to in the negative
z-direction?
(a) A conductor A
with a cavity as shown in figure (a) is given a charge Q. Show that the entire
charge must appear on the outer surfaceof the conductor. (b)
Another conductor B with charge q is inserted into the cavity keeping B
insulated from A. Show that the total charge on the outside surface of A is Q +
q [Figure (b)]. (c)
A sensitive instrument is to be shielded from the strong electrostatic fields
in its environment Suggest a possible way.
A hollow charged
conductor has a tiny hole cut into its surface. Show that the electric field in
the hole iswhere is the unit vector
in the outward normal direction, and is the surface
charge density near the hole.
Obtain the formula
for the electric field due to a long thin wire of uniform linear charge density
without using
Gauss's law. Hint. Use Coulomb's law
directly and evaluate the necessary integral.