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प्रश्न
Find the equation of the equipotentials for an infinite cylinder of radius r0, carrying charge of linear density λ.
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उत्तर
To find the potential at distance r from the line consider the electric field. We note that from symmetry the field lines must be radially outward. Draw a cylindrical Gaussian surface of radius r and length l. Then
`oint E.dS = 1/ε_0 λ1`
Or `E_r.2pirl = 1/ε_0 λ1`
⇒ `E_r = lambda/(2piε_0r)`
Hence, if r0 is the radius,
`V(r) - V(r_0) = - int_(r_0)^r E.dl = λ/(2piε_0)ln r_0/r`
For a given V,
ln `r/r_0 = - (2piε_0)/λ [V(r) - V(r_0)]`
⇒ r = r0e –2πε0Vr0/λe + 2πε0V(r)/λ
The equipotential surfaces are cylinders of radius r = r0e –2πε0[V(r) – V(r0)]/λ
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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.
The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm−1. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
What is the geometrical shape of equipotential surfaces due to a single isolated charge?
Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.
Depict the equipotential surfaces for a system of two identical positive point charges placed a distance(d) apart?
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.
Find the amount of work done in rotating an electric dipole of dipole moment 3.2 x 10- 8Cm from its position of stable equilibrium to the position of unstable equilibrium in a uniform electric field if intensity 104 N/C.
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 ______.
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.
Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately.
- 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.
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.
