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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
Two charges 2 μC and −2 µC are placed at points A and B 6 cm apart.
- Identify an equipotential surface of the system.
- What is the direction of the electric field at every point on this surface?
What is the geometrical shape of equipotential surfaces due to a single isolated charge?
Why is there no work done in moving a charge from one point to another on an equipotential surface?
Define equipotential surface.
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.
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.
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 ______.
The diagrams below show regions of equipotentials.
(i) |
(ii) |
(iii) |
(iv) |
A positive charge is moved from A to B in each diagram.
- The potential at all the points on an equipotential surface is same.
- Equipotential surfaces never intersect each other.
- Work done in moving a charge from one point to other on an equipotential surface is zero.
Equipotential surfaces ______.
Can two equipotential surfaces intersect each other?
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.
Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.
Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.
What is meant by an equipotential surface?
