A water molecule has an electric dipole moment of 6.3 x 10^-30 Cm. A sample contains 10²² water molecules, with all the dipole moments aligned parallel to the external electric field of magnitude 3 x 10⁵ NC^-1. How much work is required to rotate all the water molecules from θ = 0° to 90°? 

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.

The total number of electrons in the human body is typically in the order of 10²⁸. Suppose, due to some reason, you and your friend lost 1% of this number of electrons. Calculate the electrostatic force between you and your friend separated at a distance of 1m. Compare this with your weight. Assume mass of each person is 60 kg and use point charge approximation.

A point charge of +10 μC is placed at a distance of 20 cm from another identical point charge of +10 μC. A point charge of -2 μC is moved from point a to b as shown in the figure. Calculate the change in potential energy of the system? Interpret your result.

For the given capacitor configuration
(a) Find the charges on each capacitor
(b) potential difference across them
(c) energy stored in each capacitor

For the given circuit

Find
i) Equivalent emf
ii) Equivalent internal resistance
iii) Total current (I)
iv) Potential difference across each cell
v) Current from each cell

The resistance of a nichrome wire at 20^oC is 10 Ω. If its temperature coefficient of resistanc is 0.004^oC, find its resistance of the wire at boiling point of water. Comment on the result.

Two cells each of 5V are connected in series with a 8 Ω resistor and three parallel resistors of 4 Ω, 6 Ω, and 12 Ω. Draw a circuit diagram for the above arrangement. Calculate
(i) the current drawn from the cells
(ii) current through each resistor

Compute the work done and power delivered by the Lorentz force on the particle of charge q moving with velocity \(\vec { v } \). Calculate the angle between Lorentz force and velocity of the charged particle and also interpret the result.

An ideal transformer has 460 and 40,000 turns in the primary and secondary coils respectively. Find the voltage developed per turn of the secondary if the transformer is connected to a 230 V AC mains. The secondary is given to a load of resistance 10⁴ Ω. Calculate the power delivered to the load.

A 200 turn circular coil of radius 2 cm is placed co-axially within a long solenoid of 3 cm radius. If the turn density of the solenoid is 90 turns per cm, then calculate mutual inductance of the coil and the solenoid.

An object is placed at a certain distance from a convex lens of focal length 20 cm. Find the object distance if the image obtained is magnified 4 times.

Find the minimum thickness of a film of refractive index 1.25, which will strongly reflect the light of wavelength 589 nm. Also find the minimum thickness of the film to be anti-reflecting.

A small telescope has an objective lens of focal length 125 cm and an eyepiece of focal length 2 cm.
(a) What is the magnification of the telescope?
(b) What is the separation between the objective and the eyepiece?
(c) What is the angular separation between two stars when viewed through this telescope if they subtend 1' for bare eye?