Electrostatic Potential and Capacitance 1

Question 1

what are conservative forces

Answer 1

Forces for which potential energy is defined is called as conservative forces. The total work done against a conservative force in a round trip is 0.

Eg: Spring force, gravitational force, electrostatic force

Question 2

what is potential energy

Answer 2

Potential energy of charge q at a point (in the presence of field
due to any charge configuration) is the work done by the
external force (equal and opposite to the electric force) in
bringing the charge q from infinity to that point.

work done against electrostatic force is stored as potential energy

Question 3

what is electric potential

Answer 3

the electrostatic potential (V )
at any point in a region with electrostatic field is
the work done in bringing a unit positive
charge (without acceleration) from infinity to
that point, against electrostatic force.

unit:J/C or Volts
It is a scalar quantity

Question 4

what is potential difference

Answer 4

The potential difference betweeen any 2 pointsin an electric field is the work donein moving a unit positive charge from one point to the other.

Question 5

can there be a region with electric field but no potential

Answer 5

yes, the equatorial line of electric dipole has electric field but no electric potnetila

Question 6

can there be a region with potential but no electric field

Answer 6

yes, inside of the uniformly charged conductign sphere has no electric field but it has potential

Question 7

what does sign of work indicate

Answer 7

the work done/ sign of potential/ potential energy refers to the work done by the external force.

For a negative source charge, the work done is negative, because the work is done by the electrostatic force and is done against the external agency

for a positive source charge, the work done is positive because work is done against the electrostatic force, by the external agency.

Question 8

features of potential due to an alectric dipole

Answer 8

(i) The potential due to a dipole depends not just on r but also on the
angle between the position vector r and the dipole moment vector p.
(It is, however, axially symmetric about p. That is, if you rotate the
position vector r about p, keeping q fixed, the points corresponding
to P on the cone so generated will have the same potential as at P.)
(ii) The electric dipole potential falls off, at large distance, as 1/r
2
, not as
1/r, characteristic of the potential due to a single charge.

falls off = varies, depends

Question 9

what is equipotential surface

Answer 9

An equipotential surface is a surface with a constant value of potential
at all points on the surface.

Question 10

describe the equpotential surfaces from some things
i) point charge
ii) uniform field
iii)dipole
iv) pair of like charges

Answer 10

Now the electric field lines for a single charge q are radial lines starting
from or ending at the charge, depending on whether q is positive or negative.
Clearly, the electric field at every point is normal to the equipotential surface
passing through that point. This is true in general: for any charge
configuration, equipotential surface through a point is normal to the
electric field at that point.

i) equidistant parallel planes perpenducular to lines of force

iii) equapotential surface are closer together in the region between the 2 charges

iv) equipotential surfaces are farther apart in the region between the 2 charges indicating a weak filed in such regions

Question 11

properties of equipotential surface

Answer 11

i) The work done to displace a charge from one point to another on an equipotential surface is 0 because the potential is same at every point

ii) The electric field lines are always perpendicular to the equpotential surface.

If the field were not normal to the equipotential surface, it would
have non-zero component along the surface. To move a unit test charge
against the direction of the component of the field, work would have to
be done. But this is in contradiction to the definition of an equipotential
surface: there is no potential difference between any two points on the
surface and no work is required to move a test charge on the surface.
The electric field must, therefore, be normal to the equipotential surface
at every point.

iii) equpotential surface are closer in the regions of strong field and further apart in the regions of weak field

iv) Two equpotential surface can never intersect each other because then at the point of intersection there would be 2 potentials which is not possible