Electrostatics - Question Answers - Physics XII

Chapter – 12

Q.1: Repulsion is the sure test of electrification. Explain?
Ans: Electrostatic attraction is observed between oppositely charged bodies and also between a charged (+ve or -ve) and an uncharged body. But, however, only two charges of the same kind (both +ve or both -ve) can repel each other. Hence, repulsion is the sure test of electrification.

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Q.2: Will a solid metal sphere hold a large electric charge than a hollow sphere of the same diameter? Where the charge does resides in each case?
Ans: A solid metal sphere will hold the same amount of charge as is held by a hollow sphere of the same diameter. This is due to the fact that any excess electric charge resides only on the outer surface of a conductor.

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Q.3: Explain why it is so much easier to remove an electron from an atom of large atomic mass than it is to remove a proton?
Ans: In an atom of large atomic mass, the number of both protons and electrons is large. This big atom contains many orbits (or shells). So it is easier to remove an electron from its outermost orbit. The heavy positive nucleus exerts weaker coulomb attraction force on it as compared to an electron in the innermost shell (e.g., K shell). However, protons are in the nucleus which are held very strongly by strong nuclear forces.

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Q.4: Why is it not correct to say that potential difference is the work done in moving a unit positive charge between the points concerned?
Ans: The potential difference is the increase in electric potential energy (or work) per unit charge. So, if a small positive charge (q₀) is moved against the electric field between the two points, then the work divided by the amount of charge (w/q₀) gives the potential difference.

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Q.5: Why is it logical to say that the potential of an earth-connected object is zero? What can be said about the charge on the earth?
Ans: Practically, the earth is taken to be at zero potential. If a charged body is connected to the earth by a conductor, electron flow takes place such that the charge of the body is neutralized.

The earth is a reasonably good conductor. It is a huge neutral body. It is considered as an infinite sink to which electrons can easily migrate without changing its potential.

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Q.6: Can an electric potential exist at n point in a region where the field is zero? Can the potential be zero at a place where the electric field intensity is not zero? Give example to illustrate your reasoning.
Ans: Yes, electric potential can exist where the electric intensity is zero. The electric charge resides on the outer surface of a hollow sphere. At all points inside the sphere, the electric field intensity is zero. Otherwise, the field lines would link the charges of opposite sign in the sphere. Thus no work is done when a charge is moved between two points inside the sphere. Hence, potential is the same at all points throughout the sphere and equals that at the surface, i.e., potential is constant inside and on the surface.

• Electric potential can be zero at a point where electric intensity is not zero. For example, consider a point in the middle of two equal and opposite charges. There the electric potential is
  $V = K \, q/r + k \, -q/r = 0$

But the net electric intensity is toward the negative charge.

• Both the potential and intensity are zero for a point at infinity.

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Q.7: An air capacitor is charged to a certain potential difference. It is then immersed in oil. What happens to its (a) charge (b) potential and (c) capacitance?
Ans: The dielectric constant $\varepsilon_r$ of oil is greater than that of air. When an air capacitor is immersed in oil (after disconnecting the battery), then:

1. Its charge remains constant (since there is no path for charge transfer).
2. Potential difference between the plates decreases (and also the electric field is weakened) by a factor of $1/\varepsilon_r$.
3. The capacitance increases (since $C = q/V$) by a factor $\varepsilon_r$.

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Q.8: Two unlike capacitors of different potential and charges are joining in parallel. What happens to their potential difference? How are their charges distributed? Is the energy of the system affected?
Ans: When two unlike capacitors of different potentials and charges are joined in parallel, then:

1. The resultant potential difference will be less than the highest applied potential difference on one capacitor. This resultant potential difference will be the same for the two capacitors in parallel.
2. The charge is redistributed, and the capacitor of higher capacitance will have more charge (since $q = CV$).
3. The energy of the system will decrease. The missing energy is used in heating the wires.

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Q.9: Four similar capacitors are connected in series and joined to a 36 V battery. The mid-point of the group is earthed. What is the potential of the terminal of the group?
Ans: If two similar capacitors are connected in series, joined to a 36 V battery, and if the midpoint of the group is earthed, then there is no transfer of charge. This midpoint is between two oppositely charged plates (of $C_2$ and $C_3$). Hence the potential difference across the end of the group will remain the same (i.e., 36 V).

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Q.10: A point charge is placed at the center of a spherical Gaussian surface. Is the flux changed?

1. If the spherical Gaussian surface is replaced by a cube of the same volume.
2. If the sphere is replaced by a cube of 1/10 of this volume.
3. If the charge is moved from the center in the sphere.
4. If the charge is moved outside the sphere.

Ans:

1. No
2. No
3. No
4. Yes
5. Yes

Q.11: Four capacitors each 2μF connected in such a way that the total capacitance is also 2μF. Show what combination gives this value?
Ans: To get an equivalent capacitance of 2μF, the four capacitors, each of 2μF, can be combined in (i) two pairs of parallel combination or (ii) two pairs of series capacitors combined in parallel.

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Q.12: A capacitor is charged by a battery. The battery is disconnected and a slab of some dielectric is slipped between the plates. Describe what happens to the charge, potential difference, capacitance, and the stored energy?
Ans: When a capacitor is charged, the battery is disconnected, and a slab of some dielectric (of relative permittivity $\varepsilon_r$) is inserted, then:

1. The charge remains constant (since there is no path for transfer of the charge).
2. The potential difference decreases (and also the electric field is weakened) by a factor $\varepsilon_r$.
3. The capacitance increases (since $C = q/v$) by a factor $\varepsilon_r$.
4. The energy stored will decrease by a factor $1/\varepsilon_r$ (since, energy = $½ \, qV$), which is used in polarizing the dielectric.

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Q.13: Answer Question 12 if the battery is not disconnected?
Ans: When a capacitor is charged and the battery is not disconnected, and a slab of some dielectric (of relative permittivity $\varepsilon_r$) is increased, then:

1. The charge increases (additional charge is delivered by the battery).
2. The potential difference (and also the electric field) remains constant.
3. The capacitance increases (since $C = q/v$).
4. The energy stored will increase (since, energy $½ \, qV = ½ \, CV^2$).

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Q.14: A capacitor is connected across a battery. Why does each plate receive a charge of the same magnitude? Will it be true if the plates are of different sizes?
Ans: When a capacitor is connected to a battery, such that +ve, terminal ‘b’ is at a higher potential than the plate B, then electrons are drawn toward, ‘b’ from B. However, the -ve terminal ‘a’ is at potential than the plate A, so the electrons are drawn the plate A from ‘a’. Thus B is positively charged. The charging stops when $V_{AB} = V$. If the sizes of the plates are different, then the plate of larger area will receive more amount of charge.

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Q.15: Write electric field statements analogous to the following in gravitational field. 1. Water flows from a higher level to a lower level; 2. Water always maintains its level; 3. The total mass is conserved; 4. When a body falls through a height ‘h’ it loses potential energy and gains kinetic energy?
Ans: The analogous statements are:

1. Electric charge flows from a higher potential to a lower potential.
2. Charge always maintains its potential.
3. The total charge is conserved.
4. When a charge body falls through a potential difference, it loses its electrical potential energy and gains kinetic energy.

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Q.16: Is it true that “an alternating current can pass through a capacitor while a direct current”. Explain?
Ans: A capacitor is said to ‘block’ direct current or voltage. That is, there is no current through a capacitor by a steady direct voltage. However, when the capacitor is connected across an a.c supply, the capacitor (or plates) are continuously charged and discharged (during alternate quarter cycle), and charged the other way round by the alternating voltage. The current thus flows round the circuit. A capacitance that allows alternating current offers opposition (in ohms), called capacitive reactance (X-C).

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Q.17: The unit of permittivity $C^2 \, N^{-1} \, m^{-2}$ is the same as $F \, m^{-1}$ how?
Ans: $F = \frac{M}{L \, T^2} \times C^2 \times \frac{1}{m} = \frac{C^2}{J/C \times m} = \frac{C^2}{N.m} = \frac{C^2}{N.m^2}$.

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Q.18: What happens if a charge is moved in an electric field?
Ans: A charge is displaced in two ways:

1. Against the electric field (say from point A to B): then work is done on the charge. This increase electric potential energy thus i (P.E.) = qΔV.
2. In the direction of the electric field (from B to A): then p.c. decreases which appears as increase in K.E. thus (K.E.) = ½ mv^2.

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Q.19: What will be the flux through a closed surface which does not contain any charge?
Ans: As the surface encloses no charge, so the flux is zero. From Gauss's Law: $\phi = q/\varepsilon_0 = 0/\varepsilon_0 = 0$

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Q.20: What is the flux, electric field intensity and potential inside a charged sphere?
Ans: Both the flux and the intensity are zero inside a charged sphere. The potential inside a charged sphere is the same as at its surface.

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Q.21: An uncharged conducting spherical shell is placed in the field of a positive charge q. what will be the net flux through the shell? What is the unit of electric flux?
Ans: According to Gauss’ law, the net flux through the shell will be zero as then it contains no charge. The SI unit of electric flux is $\text{N m}^2 \text{ C}^{-1}$.

Q.22: Is electrical p.d. same as electrical p.e?
Ans: No, electrical p.e. is the total work done in moving a certain charge $q$ from one point to another against electric intensity.
Thus, $U_B - U_A = W_A \rightarrow B = \Delta W$

Electric p.d. is the work done in moving a unit positive charge from one point to another against electric intensity.
Since $V_B - V_A = \Delta W/q_0 = \Delta U/q_0$

Now, a relation between them is: $U = q_0 \, \Delta V$

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Q.23: Why is water not used as a dielectric?
Ans: The near impossibility of removing all impurities dissolved in water makes it unsuitable in practice as a dielectric.