Advertisements
Advertisements
Question
The work done to move a charge along an equipotential from A to B ______.
- cannot be defined as `- int_A^B E.dl`
- must be defined as `- int_A^B E.dl`
- is zero.
- can have a non-zero value.
Options
a and b
b and c
c and d
a and c
Advertisements
Solution
b and c
Explanation:
The work done by the external agent in shifting the test charge along the dashed line from 1 to 2 is
|
The external agent does a work `W = - q int_1^2 vecE * vec(dl)` in transporting the test charge q slowly from the positions 1 to 2 in the static electric field. |
`W_("ext") = int_1^2 vecF_("ext") * vec(dl) int_1^2 (-qvecE) * vec(dl) = - q int_1^2 vecE * vec(dl)`
We know `V_A - V_B = - int_A^B vecE * vec(dl)` ......(i)
`W_("electrical") = -ΔU = - qΔV = q(V_A - V_B)` ......(ii)
Hence from (i) and (ii), `W_("electrical") = q(V_A - V_B) = - qint_A^B vecE * vec(dl)`
If we want to calculate the work done to move a charge along an equipotential from A to B
For equipotential surface VA = VB, hence W = 0
Also electric field is perpendicular to equipotential surface, hence `vecE * vec(dl) => W_("electrical") = 0`
APPEARS IN
RELATED QUESTIONS
A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1 m2. Will he get an electric shock if he touches the metal sheet next morning?
Draw equipotential surfaces:
(1) in the case of a single point charge and
(2) in a constant electric field in Z-direction. Why are the equipotential surfaces about a single charge not equidistant?
(3) Can electric field exist tangential to an equipotential surface? Give reason
Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
Define equipotential surface.
Draw the equipotential surfaces due to an electric dipole.
Depict the equipotential surface due to
(i) an electric dipole,
(ii) two identical positive charges separated by a distance.
A particle of mass 'm' having charge 'q' is held at rest in uniform electric field of intensity 'E'. When it is released, the kinetic energy attained by it after covering a distance 'y' will be ______.
Assertion: Electric field is discontinuous across the surface of a spherical charged shell.
Reason: Electric potential is continuous across the surface of a spherical charged shell.
Consider the following statements and select the correct statement(s).
- Electric field lines are always perpendicular to equipotential surface.
- No two equipotential surfaces can intersect each other.
- Electric field lines are in the direction of tangent to an equipotential surface.
The diagrams below show regions of equipotentials.
(i) |
(ii) |
(iii) |
(iv) |
A positive charge is moved from A to B in each diagram.
Equipotential surfaces ______.
Can two equipotential surfaces intersect each other?
Consider a uniform electric field in the ẑ direction. The potential is a constant ______.
- in all space.
- for any x for a given z.
- for any y for a given z.
- on the x-y plane for a given z.
Equipotential surfaces ______.
- are closer in regions of large electric fields compared to regions of lower electric fields.
- will be more crowded near sharp edges of a conductor.
- will be more crowded near regions of large charge densities.
- will always be equally spaced.
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
What is meant by an equipotential surface?
