Advertisements
Advertisements
प्रश्न
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.
पर्याय
a and b
b and c
c and d
a and c
Advertisements
उत्तर
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
संबंधित प्रश्न
Define an equipotential surface.
A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.
Describe schematically the equipotential surfaces corresponding to
(a) a constant electric field in the z-direction,
(b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction,
(c) a single positive charge at the origin, and
(d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.
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?
What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
(Hint: The earth has an electric field of about 100 Vm−1 at its surface in the downward direction, corresponding to a surface charge density = −10−9 C m−2. Due to the slight conductivity of the atmosphere up to about 50 km (beyond which it is good conductor), about + 1800 C is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)
What is the geometrical shape of equipotential surfaces due to a single isolated charge?
Two identical point charges, q each, are kept 2m apart in the air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q.
Draw the equipotential surfaces due to an electric dipole.
Write two important characteristics of equipotential surfaces.
Statement - 1: For practical purpose, the earth is used as a reference at zero potential in electrical circuits.
Statement - 2: The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by `Q/(4piepsilon_0R)`.
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.
Equipotential surfaces ______.
Can two equipotential surfaces intersect each other?
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.
