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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?
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उत्तर
Given: q1 = 2 μC = 2 × 10−6 C
q2 = −2 µC = 2 × 10−6 C
r = 6 cm = 0.06 m
(a) Potential will be zero due to both charges at the equipotential surface.
`1/(4piε_0)[q_1/x + q_2/((0.06 - x))] = 0`
`q_1/x = -q_2/((0.06 - x))`
`(2 xx 10^-6)/x = -((-2 xx 10^-6))/([(0.06) - x])`
x = 0.06 − x
x + x = 0.06
2x = 0.06
`x = 0.06/2`
x = 0.03 m
i.e., the plane normal to AB and passing through its mid-point has zero potential everywhere.
(b) The direction of the electric field at every point on this surface is normal to the plane in the direction of AB.
संबंधित प्रश्न
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 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?
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.
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.
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.
Which of the following is NOT the property of equipotential surface?
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.
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.
Find the equation of the equipotentials for an infinite cylinder of radius r0, carrying charge of linear density λ.
Draw equipotential surfaces for (i) an electric dipole and (ii) two identical positive charges placed near each other.
