A rectangular coil of n turns each of area A, carrying current I, when suspended in a uniform magnetic field B, experiences a torque
\(\tau =nI \ BA \ sin\theta \)
Where is \(\theta \) the angle which a normal drawn on the plane of coil makes with the direction of magnetic field. This torque tends to rotate the coil and bring it in an equilibrium position. In the stable equilibrium state, the resultant force on the coil is zero. The torque on the coil is also zero and the coil has minimum potential energy.
Read the above passage and answer the following questions:
(i) In which position, a current carrying coil suspended in uniform magnetic field experiences
(a) minimum torque and
(b) maximum torque?
(ii) a circular coil of 200 turns, radius 5 cm carries a current of 2.0 A. It is suspended vertically in a uniform horizontal magnetic field of 0.20 T, with the plane of the coil making an angle with \(60°\) the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning.
(iii) what is the basic value displayed by the above study?

Derive the expression for the energy stored in parallel plate capacitor. Hence, obtain the expression for the energy density of the electric field.
A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than stored initially in the single capacitor.

In Akash's classroom the fan above the teacher was running very slowly. Due to which his teacher was sweating and was restless and tired. All his classmates wanted to rectify this. They called for an electrician who came and changed the capacitor only after which the fan started running fast.
(a) What values did Akash and his classmates have?
(b) What energy is stored in the capacitor and where?

Two point charges \(+4\mu C\) and \(-6\mu C\) are separated by a distance of 20cm in air. At what point on the line joining the two charges is the electric potential zero?

A series LCR circuit with L = 80mH, C = 50\(\mu\)F and R = 60 ohm is connected to a variable frequency 220V source. Determine
(i) the source frequency which drive the circuit in resonance
(ii) the quality factor Q of the circuit.

A thin prism of refracting angle \(2°\) deviates an incident ray through an angle of \(1°\). Find the value of refractive index of material of prism.

A monochromatic source, emitting light of wavelength, 600 nm, has a power output of 66W. Calculate the number of photons emitted by this source in 2 minutes. Use, h = 6.63 x 10^-34J

It is estimated that the atomic bomb exploded at Hiroshima released a total energy of \(7.6\times { 10 }^{ 13 }\)J. If on the average, 200MeV energy was released per fission, calculate 
(i) the number of Uranium atoms fissioned.
(ii) the mass of Uranium used in the bomb.

A TV transmitting antenna is tall. How much service area this transmitting antenna cover, if the receiving antenna is at the ground level? Radius of earth = 6400 km.