Consider two point charges q₁ and q₂ at rest as shown in the figure.

They are separated by a distance of 1m. Calculate the force experienced by the two charges for the following cases:
(a) q₁ = +2μC and q₂ = +3μC
(b) q₁ = +2μC and q₂ = -3μC
(c) q₁= +2μC and q₂ = -3μC kept in water (ε_r = 80)

Two small-sized identical equally charged spheres, each having mass 1 g are hanging in equilibrium as shown in the figure. The length of each string is 10 cm and the angle θ is 30° with the vertical. Calculate the magnitude of the charge in each sphere. (Take g = 10 ms⁻²)

Calculate the electrostatic force and gravitational force between the proton and the electron in a hydrogen atom. They are separated by a distance of 5.3 x 10^–11 m. The magnitude of charges on the electron and proton are 1.6 x 10^–19 C. Mass of the electron is m_e = 9.1 x 10^–31 kg and mass of proton is m_p = 1.6 x 10^–27 kg.

Consider four equal charges q₁, q₂, q₃ and q₄ = q = +1 μC located at four different points on a circle of radius 1m, as shown in the figure. Calculate the total force acting on the charge q₁ due to all the other charges.

Calculate the electric field at points P, Q for the following two cases, as shown in the figure.
(a) A positive point charge +1 μC is placed at the origin.
(b) A negative point charge -2 μC is placed at the origin.

(a) Calculate the electric potential at points P and Q as shown in the figure below.
(b) Suppose the charge + 9μC is replaced by - 9 μC find the electrostatic potentials at points P and Q.

(c) Calculate the work done to bring a test charge +2 μC from infinity to the point Q. Assume the charge +9 μC is held fixed at origin and +2 μC is brought from infinity to P.

A small ball of conducting material having a charge +q and mass m is thrown upward at an angle θ to horizontal surface with an initial speed v_o as shown in the figure. There exists an uniform electric field E downward along with the gravitational field g. Calculate the range, maximum height and time of flight in the motion of this charged ball. Neglect the effect of air and treat the ball as a point mass.

A parallel plate capacitor has square plates of side 5 cm and separated by a distance of 1 mm.
(a) Calculate the capacitance of this capacitor.
(b) If a 10 V battery is connected to the capacitor, what is the charge stored in any one of the plates? (The value of ε_o = 8.85 x 10^-12 Nm² C^-2)

A parallel plate capacitor filled with mica having ε_r = 5 is connected to a 10 V battery. The area of the parallel plate is 6 cm² and separation distance is 6 mm.
(a) Find the capacitance and stored charge.
(b) After the capacitor is fully charged, the battery is disconnected and the dielectric is removed carefully.
Calculate the new values of capacitance, stored energy and charge.

Find the equivalent capacitance between P and Q for the configuration shown below in the figure (a).

Two conducting spheres of radius r₁ = 8 cm and r₂ = 2 cm are separated by a distance much larger than 8 cm and are connected by a thin conducting wire as shown in the figure. A total charge of Q = +100 nC is placed on one of the spheres. After a fraction of a second, the charge Q is redistributed and both the spheres attain electrostatic equilibrium.

(a) Calculate the charge and surface charge density on each sphere.
(b) Calculate the potential at the surface of each sphere.

What are the differences between Coulomb force and gravitational force?

Five identical charges Q are placed equidistant on a semicircle as shown in the figure. Another point charge q is kept at the center of the circle of radius R. Calculate the electrostatic force experienced by the charge q.

Suppose a charge +q on Earth’s surface and another +q charge is placed on the surface of the Moon.
(a) Calculate the value of q required to balance the gravitational attraction between Earth and Moon.
(b) Suppose the distance between the Moon and Earth is halved, would the charge q change?
(Take m_E = 5.9 x 10²⁴ kg, m_M = 7.9 x 10²² kg)

The electrostatic potential is given as a function of x in figure (i) and (ii). (a) Calculate the corresponding electric fields in regions A, B, C and D for the Figure (i). (b) Plot the electric field as a function of x for the figure (ii).

A spark plug in a bike or a car is used to ignite the air-fuel mixture in the engine. It consists of two electrodes separated by a gap of around 0.6 mm gap as shown in the figure.

To create the spark, an electric field of magnitude 3 x 10⁶ Vm^-1 is required.
(a) What potential difference must be applied to produce the spark?
(b) If the gap is increased, does the potential difference increase, decrease or remains the same?
(c) find the potential difference if the gap is 1 mm.

Calculate the resultant capacitances for each of the following combinations of capacitors.

An electron and a proton are allowed to fall through the separation between the plates of a parallel plate capacitor of voltage 5 V and separation distance h = 1 mm as shown in the figure.

(a) Calculate the time of flight for both electron and proton
(b) Suppose if a neutron is allowed to fall, what is the time of flight?
(c) Among the three, which one will reach the bottom first? (Take m_p = 1.6 x 10^-27 kg, m_e = 9.1 x 10^-31 kg and g = 10 m s^-2)