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प्रश्न
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.
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उत्तर
The given figure shows six equal amounts of charges q at the vertices of a regular hexagon.
Where,
Charge, q = 5 µC = 5 × 10−6 C
Side of the hexagon, l = AB = BC = CD = DE = EF = FA = 10 cm
Distance of each vertex from centre O,
d = 10 cm
Electric potential at point O,
`V = (6 xx q)/(4pi ε_0 d)`
Where,
`ε_0` = Permittivity of free space
`1/(4pi ε_0) = 9 xx 10^9` N C−2 m−2
∴ `V = (6 xx 9 xx 10^9 xx 5 xx 10^-6)/0.1`
= 270 × 103
= 2.7 × 106 V
Therefore, the potential at the centre of the hexagon is 2.7 × 106 V.
संबंधित प्रश्न
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.
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.
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 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.
Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.
Equipotential surfaces are shown in figure. Then the electric field strength will be ______.
In the hierarchy of equipotential concepts, which term describes a volume enclosed at the same potential?
If the electric field \[\vec{E}\] had a component along (tangent to) an equipotential surface, what contradiction would arise?
Equipotential surfaces are denser (closer together) in regions where:
What is the shape of the equipotential surfaces for a single point charge (+q)?
For an infinite line charge (infinite cylinder configuration), the equipotential surfaces are:
In a uniform electric field, the equipotential surfaces take the shape of:
In the derivation proving \[\vec{E}\] is perpendicular to an equipotential surface, a charge \[q_0\] undergoes a small displacement \[d\vec{l}\] along the surface, with \[\vec{E}\] making an angle \[\theta\] with the displacement. Equating the work expressions leads to which conclusion?
The relation between the electric field \[\vec{E}\] and the potential gradient is expressed as:
