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 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.

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)

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

A copper slab of mass 2g contains 2 x 10²² atoms. The charge on the nucleus of each atom is 29 e. What fraction of the electrons must be removed from the sphere to give it a charge of +2μC?

The electric potential in region is represented as V = 2x + 3y - z. Obtain an expression for electric field strength.

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

Find the heat energy produced in a resistance of 10 Ω when 5 A current flows through it for 5 minutes.

The current through an element is shown in the figure. Determine the total charge that pass through the element at a) t = 0 s, b) t = 2 s, c) t = 5s

I - V graph for a metallic wire at two different temperatures T₁ & T₂ as shown in figure. Which of the two temperature is lower. Why?

An aluminium wire of diameter 0.24 cm is connected in series to a copper wire of diameter 0.16 cm. The wires carry an electric current of 10 A. Determine the current density in aluminium wire.

Calculate the magnetic field inside a solenoid, when
(a) the length of the solenoid becomes twice with fixed number of turns
(b) both the length of the solenoid and number of turns are doubled
(c) the number of turns becomes twice for the fixed length of the solenoid.
Compare the results.

The coil of a moving coil galvanometer has 5 turns and each turn has an effective area of 2 x 10^–2 m². It is suspended in a magnetic field whose strength is 4 x 10^–2 Wb m^–2. If the torsional constant K of the suspension fibre is 4 x 10^–9 N m deg^–1.
(a) Find its current sensitivity in division per microampere.
(b) Calculate the voltage sensitivity of the galvanometer for it to have full scale deflection of 50 divisions for 25 mV.
(c) Compute the resistance of the galvanometer

An inverter is common electrical device which we use in our homes. When there is no power in our house, inverter gives AC power to run a few electronic appliances like fan or light. An inverter has inbuilt step-up transformer which converts 12 V AC to 240 V AC. The primary coil has 100 turns and the inverter delivers 50 mA to the external circuit. Find the number of turns in the secondary and the primary current.

Write down the equation for a sinusoidal voltage of 50 Hz and its peak value is 20 V. Draw the corresponding voltage versus time graph.

The equation for an alternating current is given by i = 77 sin 314t. Find the peak current, frequency, time period and instantaneous value of current at t = 2 ms.

A long solenoid having 400 turns per cm carries a current 2A. A 100 turn coil of cross-sectional area 4 cm² is placed co-axially inside the solenoid so that the coil is in the field produced by the solenoid. Find the emf induced in the coil if the current through the solenoid reverses its direction in 0.04 sec.

Explain the mechanical analogy of LC oscillations by quantitative treatment.

Consider a parallel plate capacitor whose plates are closely spaced. Let R be the radius of the plates and the current in the wire connected to the plates is 5 A, calculate the displacement current through the surface passing between the plates by directly calculating the rate of change of flux of electric field through the surface.

A diffraction grating consists of 4000 slits per centimeter. It is illuminated by a monochromatic light. The second order diffraction maximum is produced at an angle of 30°. What is the wavelength of the light used?

Half lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. Calculate the ratio of decayed numbers of A and B nuclei after 80 minutes.

On your birthday, you measure the activity of the sample ²¹⁰Bi which has a half-life of 5.01 days. The initial activity that you measure is 1µCi.
(a) What is the approximate activity of the sample on your next birthday? Calculate
(b) the decay constant
(c) the mean life
(d) initial number of atoms.

A radioactive sample has 2.6μg of pure \(_{ 7 }^{ 13 }{ N }\) which has a half-life of 10 minutes.
(a) How many nuclei are present initially?
(b) What is the activity initially?
(c) What is the activity after 2 hours? (d) Calculate mean life of this sample.

Calculate the amount of energy released when 1 kg of \(_{ 92 }^{ 235 }{ U }\) undergoes fission reaction.