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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
Define an equipotential surface.
Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge
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.
What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning?
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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
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.
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Depict the equipotential surface due to
(i) an electric dipole,
(ii) two identical positive charges separated by a distance.
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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)`.
S1 and S2 are the two imaginary surfaces enclosing the charges +q and -q as shown. The electric flux through S1 and S2 are respectively ______.
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Reason: Electric potential is continuous across the surface of a spherical charged shell.
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.
Find the equation of the equipotentials for an infinite cylinder of radius r0, carrying charge of linear density λ.
What is meant by an equipotential surface?
