Electrostatic Potential and Capacitance Physics - Electrostatic Potential and Capacitance

Two charges 2 µC and –2 µC are placed at points A and B 6 cm apart.

1. Identify an equipotential surface of the system.
2. What is the direction of the electric field at every point on this surface?

In a Van de Graaff type generator a spherical metal shell is to be a 15 × 10⁶V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 10⁷Vm^–1. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

A small sphere of radius r₁ and charge q₁ is enclosed by a spherical shell of radius r₂ and charge q₂. Show that if q₁ is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q₂ on the shell is.

Three capacitors each of capacitance 9 pF are connected in series.

1. What is the total capacitance of the combination?
2. What is the potential difference across each capacitor if the combination is connected to a 120 V supply?

Answer the following:
The discharging current in the atmosphere due to the small conductivity of air is known to be 1800A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?

A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10^–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field:

1. Inside the sphere
2. Just outside the sphere
3. At a point 18 cm from the centre of the sphere?

Answer carefully:
What meaning would you give to the capacitance of a single conductor?

Answer carefully:
A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?

Answer the following:
The top of the atmosphere is at about 400kV 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 100Vm^–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!)

Answer carefully:
Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

The mean free path of electrons in a gas in a discharge tube is inversely proportional to the pressure inside it. The Crookes dark space occupies half the length of the discharge tube when the pressure is 0.02mm of mercury. Estimate the pressure at which the dark space will fill the whole tube.

A tungsten cathode and a thoriated-tungsten cathode have the same geometric dimensions and are operated at the same temperature. The thoriated-tungsten cathode gives 5000 times more current than the other cathode. Find the operating temperature. Take relevant data from the previous problem.

The saturation current from a thoriated-tungsten cathode at 2000K is 100mA. What will be the saturation current for a pure-tungsten cathode of the same surface area operating at the same temperature? The constant A in the Richardson-Dushman equation is 60 × 10⁴Am^-2K^-2 for pure tungsten and 3.0 × 10⁴Am^-2k^-2 for thoriated tungsten. The work function of pure tungsten is 4.5eV and that of thoriated tungsten is 2.6eV.

A point charge is situated at an axial point of a small electric dipole at a large distance from it. The charge experiences a force F. If the distance of the charge is doubled, the force acting on the charge will become:

Dielectrics are ____ substances.

For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

1. Both A and R are true, and R is the correct explanation of A.
2. Both A and R are true, but R is not the correct explanation of A.
3. A is true, but R is false.
4. A is false, and R is also false.

Assertion (A): Positive charge always moves from a higher potential point to a lower potential point.
Reason (R): Electric potential is a vector quantity.

For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

1. Both A and R are true, and R is the correct explanation of A.
2. Both A and R are true, but R is not the correct explanation of A.
3. A is true, but R is false.
4. A is false, and R is also false.

Assertion (A): The surface of a conductor is an equipotential surface.
Reason (R): Conductor allows the flow of charge.

For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

1. Both A and R are true, and R is the correct explanation of A.
2. Both A and R are true, but R is not the correct explanation of A.
3. A is true, but R is false.
4. A is false, and R is also false.

Assertion (A): A capacitor is connected to a battery. If we move its plate further apart, work will be done against the electrostatic attraction between the plates, and the energy of the capacitor gets decreased.
Reason (R): The energy stored in capacitor is dissipated in the form of heat energy.

For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

1. Both A and R are true, and R is the correct explanation of A.
2. Both A and R are true, but R is not the correct explanation of A.
3. A is true, but R is false.
4. A is false, and R is also false.

Assertion (A): The whole charge of a conductor cannot be transferred to another isolated conductor.
Reason (R): The total transfer of charge from one to another is not possible.

For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.

1. Both A and R are true, and R is the correct explanation of A.
2. Both A and R are true, but R is not the correct explanation of A.
3. A is true, but R is false.
4. A is false, and R is also false.

Assertion (A): When a dielectric medium is filled between the plates of a condenser, its capacitance increases.
Reason (R): The dielectric medium reduces the potential difference between the plates of the condenser.

A 600pF capacitor is charged by a 200V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

Two charges 5 × 10^–8 C and –3 × 10^–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with thatdue to an electric dipole, and an electric monopole (i.e., a single charge).