1.Why can one safely ignore the quantization of electric charge when dealing with macroscopic (large-scale) charges?
2.A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}\text{ C}$. Estimate the number of electrons transferred, and explicitly state from which to which substance they moved.
3.In the context of Q2, is there a physical transfer of mass from wool to polythene? If yes, calculate the exact mass transferred. (Given $m_e = 9.1 \times 10^{-31}\text{ kg}$).
4.Two identical metallic spheres A and B, mounted on insulated stands, carry charges $+Q$ and $-3Q$ respectively. They are brought into contact and then separated to the same distance. What is the new charge on each sphere?
5.A glass rod when rubbed with silk acquires a charge of $+1.6 \times 10^{-12}\text{ C}$. Calculate the amount of charge that appears on the silk cloth and justify your answer using a fundamental law of electrostatics.
6.Explain briefly the mechanism by which an uncharged conducting sphere can be permanently positively charged using the method of induction.
7.Can a charged body theoretically possess a total charge of $0.32 \times 10^{-18}\text{ C}$? Provide mathematical reasoning to support your answer.
8.How does the principle of charge additivity apply to a system consisting of continuous charge distribution instead of discrete point charges?
9.Two identical charges repel each other with a force equal to the weight of a $10\text{ mg}$ mass when they are $0.6\text{ m}$ apart in a vacuum. Find the magnitude of each charge. (Take $g = 10\text{ m/s}^2$).
10.Two point charges $q_1 = +2 \mu\text{C}$ and $q_2 = -2 \mu\text{C}$ are placed at coordinates $(0,0,0)$ and $(3,4,0)\text{ m}$ respectively. Calculate the force vector acting on $q_2$ due to $q_1$.
11.Two point charges placed at a certain distance $r$ in air exert a force $F$ on each other. If they are immersed in a liquid of dielectric constant $K=80$ while keeping the distance unchanged, what is the new force between them in terms of $F$?
12.A charge $q$ is placed at the exact center of the line joining two equal charges $Q$. Show analytically that the entire system of three charges will be in equilibrium only if $q = -Q/4$.
13.Plot a graph showing the variation of Coulomb force ($F$) versus $1/r^2$, where $r$ is the distance between two fixed point charges. What physical quantity does the slope of this graph represent?
14.Three identical point charges, each of magnitude $q$, are placed at the vertices of an equilateral triangle of side $a$. Determine the magnitude of the net electrostatic force acting on any one of the charges.
15.How does the electrostatic force between two point charges change if a metallic slab is completely inserted between them? Explain.
16.Compare the relative strengths of the electrostatic force and the gravitational force between two protons. Which one dominates at atomic scales?
17.Four point charges $+q, -q, +q, -q$ are placed at the corners A, B, C, and D respectively of a square of side $a$. Calculate the net electric field vector at the geometric center of the square.
18.An electron falls from rest through a vertical distance of $1.5\text{ cm}$ in a uniform downward electric field of magnitude $2.0 \times 10^4\text{ N/C}$. Calculate the time taken for it to fall. (Given $m_e = 9.1 \times 10^{-31}\text{ kg}$).
19.A charged oil drop of mass $9.9 \times 10^{-15}\text{ kg}$ remains stationary in a uniform vertically downward electric field of $3 \times 10^4\text{ V/m}$. Find the charge on the drop and the number of excess or deficit electrons. (Take $g=10\text{ m/s}^2$).
20.Sketch the electric field lines for a system consisting of two identical positive point charges $+q$ separated by a small distance. Clearly mark the position of the null point.
21.Why is the electric field strictly zero everywhere inside a hollow charged conductor, regardless of its shape, under static conditions?
22.Define a 'null point' in an electric field. Where does the null point lie between two unequal, opposite charges?
23.Two point charges $q_1$ and $q_2$ are placed $30\text{ cm}$ apart. The electric field at the midpoint of the line joining them is zero. What can you definitively conclude about the magnitudes and signs of $q_1$ and $q_2$?
24.Explain why electrostatic field lines cannot have sudden breaks or discontinuities in a charge-free region.
25.Derive the expression for the electric field at a point on the equatorial plane of an electric dipole. From this, deduce the field for a very short dipole.
26.An electric dipole of length $2\text{ cm}$ is placed with its axis making an angle of $60^\circ$ with respect to a uniform electric field of $10^5\text{ N/C}$. If it experiences a torque of $8\sqrt{3}\text{ Nm}$, calculate the magnitude of the charge on the dipole.
27.Using the data from Q26, calculate the potential energy of the dipole in that orientation.
28.Calculate the electric flux through a planar surface area $\vec{A} = (2\hat{i} + 3\hat{j})\text{ m}^2$ kept in a uniform electric field $\vec{E} = (5\hat{i} + 4\hat{j} - \hat{k})\text{ V/m}$.
29.Show theoretically that for a short electric dipole, the magnitude of the electric field at an axial point is twice the magnitude of the field at an equatorial point at the same distance.
30.If an electric dipole is placed in a strongly non-uniform electric field, describe the nature of the translational force and torque it will experience.
31.What is the net electric flux passing through a closed hemispherical surface of radius $R$ placed in a uniform electric field $\vec{E}$ parallel to its circular base?
32.A point charge $Q$ is placed at one of the corners of a cube. What is the total electric flux passing through the cube?
33.State Gauss's Law. Using Gauss's Law, deduce the expression for the electric field due to a uniformly charged thin spherical shell of radius $R$ at a point outside the shell ($r > R$).
34.Two concentric spherical conducting shells of radii $R_1$ and $R_2$ ($R_1 < R_2$) enclose charges $Q_1$ and $Q_2$ respectively. Find the ratio of the total electric flux passing through the inner shell to that passing through the outer shell.
35.If the net electric flux passing out of a closed surface is zero, does it definitively mean that the electric field is zero at all points on the surface? Justify your answer.
36.A large metallic plane has a surface charge density of $2.0 \times 10^{-6}\text{ C/m}^2$. Calculate the total electric flux crossing a circular area of radius $0.5\text{ m}$ parallel to the plane.
37.Define volume charge density ($\rho$). If a solid non-conducting sphere of radius $R$ has a uniform volume charge density $\rho$, write the expression for the total charge $Q$ inside the sphere.
38.A charge $q$ is uniformly distributed over a ring of radius $a$. Find the linear charge density of the ring.
39.A point charge of $2.0 \mu\text{C}$ is at the center of a cubic Gaussian surface $9.0\text{ cm}$ on edge. What is the net electric flux through the surface?
40.How would the electric flux through a spherical Gaussian surface change if the point charge enclosed within it is moved off-center, but still inside the sphere?
41.Use Gauss's law to derive the expression for the electric field intensity due to a uniformly charged infinite plane sheet of surface charge density $\sigma$.
42.Two large, thin parallel metal plates have surface charge densities of opposite signs and magnitude $17.0 \times 10^{-22}\text{ C/m}^2$. Calculate the electric field in the region strictly between the two plates.
43.Referring to Q42, what is the electric field in the outer region of the first plate (above both plates)? Provide the theoretical reasoning.
44.A long straight wire has a uniform linear charge density of $2 \times 10^{-4}\text{ C/m}$. Calculate the magnitude of the electric field at a perpendicular distance of $10\text{ cm}$ from the wire.
45.Plot a generic graph showing the variation of electric field $E$ with distance $r$ from the center of a uniformly charged solid conducting sphere of radius $R$.
46.A charged particle of mass $m$ and charge $q$ is released from rest in the electric field of an infinite line charge. Will its acceleration be constant? Explain.
47.A spherical shell has a radius $R$ and uniform surface charge density $\sigma$. Using Gauss’s law, prove that the electric field inside the shell is zero everywhere.
48.Why does the electric field due to an infinite uniformly charged sheet remain independent of the distance from the sheet? Explain based on field lines or symmetry.
