Electric fields and charges 3

Question 1

COULOMB’S LAW

Answer 1

Coulomb measured the
force between two point charges and found that it varied inversely as
the square of the distance between the charges and was directly
proportional to the product of the magnitude of the two charges and acted along the line joining the two charges. Thus, if two
point charges q1
, q2
are separated by a distance r in vacuum,
the magnitude of the force (F) between them is given by

Question 2

How did Coulomb arrive at this law from his experiments?

Answer 2

• Coulomb used a torsion balance* for measuring the force
  between two charged metallic spheres. When the separation
  between two spheres is much larger than the radius of each
  sphere, the charged spheres may be regarded as point charges.
• he discover a relation Coulomb thought of the following simple way: Suppose the
  charge on a metallic sphere is q. If the sphere is put in contact
  with an identical uncharged sphere, the charge will spread over
  the two spheres. By symmetry, the charge on each sphere will
  be q/2*. Repeating this process, we can get charges q/2, q/4,
  etc. Coulomb varied the distance for a fixed pair of charges and
  measured the force for different separations. He then varied the
  charges in pairs, keeping the distance fixed for each pair.
  Comparing forces for different pairs of charges at different
  distances, Coulomb arrived at the relation

Question 3

1 C

Answer 3

1 C is the charge that when placed at a distance
of 1 m from another charge of the same magnitude in vacuum
experiences an electrical force of repulsion of magnitude 9 × 10^9 N.

Question 4

ɛ̝0

Answer 4

• is called the permittivity of free space
• 8.854 × 10^(–12) C^2N–1m–2

Question 5

Coulomb’s law gives

Answer 5

the force between two charges q1
and
q2
in vacuum. If the charges are placed in matter or the intervening
space has matter, the situation gets complicated due to the presence
of charged constituents of matter.

Question 6

principle of superposition.

Answer 6

Experimentally, it is verified that force on any charge due
to a number of other charges is the vector sum of all the forces
on that charge due to the other charges, taken one at a time.
The individual forces are unaffected due to the presence of
other charges. This is termed as the principle of superposition.

Question 7

The word “field” signifies

Answer 7

The word “field” signifies how some distributed quantity (which
could be a scalar or a vector) varies with position. The effect of the charge
has been incorporated in the existence of the electric field

Question 8

define electric field

Answer 8

• the
  electric field due to a charge Q at a point in space may be defined
  as the force that a unit positive charge would experience if placed at that point. - The charge Q, which is producing the electric field, is
  called a source charge and the charge q, which tests the effect of a
  source charge, is called a test charge.

Question 9

the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q. why?

Answer 9

the electric field E due to Q, though defined operationally in
terms of some test charge q, is independent of q. This is because
F is proportional to q, so the ratio F/q does not depend on q. The
force F on the charge q due to the charge Q depends on the particular
location of charge q which may take any value in the space around
the charge Q. Thus, the electric field E due to Q is also dependent on
the space coordinate r. For different positions of the charge q all over
the space, we get different values of electric field E. The field exists at
every point in three-dimensional space.

Question 10

direction of electric field for +ve and -ve charges

Answer 10

For a positive charge, the electric field will be directed radially
outwards from the charge. On the other hand, if the source charge is
negative, the electric field vector, at each point, points radially inwards.

Question 11

The magnitude of electric field E due to
a point charge has a spherical symmetry. justify.

Answer 11

Since the magnitude of the force F on charge q due to charge Q
depends only on the distance r of the charge q from charge Q,
the magnitude of the electric field E will also depend only on the
distance r. Thus at equal distances from the charge Q, the magnitude
of its electric field E is same. The magnitude of electric field E due to
a point charge is thus same on a sphere with the point charge at its
centre; in other words, it has a spherical symmetry.