State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.
An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4  Nm. Calculate the potential energy of the dipole, if it has charge ±8 n C.Â
Given,
Length of the dipole, l = 4 cmÂ
Torque,  = 4 N m
Using the formula for torque, we have
Torque, τ = PEsinθ = (Ql) Esinθ                                       ...(1) Â
Potential energy, U= −PEcosθ= −(Ql)Ecosθ                   ...(2)
Dividing equation (2) by (1),
A potentiometer wire of length 1 m has a resistance of 10 Ω. It is connected to a 6 V battery in series with a resistance of 5 Ω. Determine the emf of the primary cell which gives a balance point at 40 cm.Â
(a) Obtain the expression for the energy stored per unit volume in a charged parallel plate capacitor.
(b) The electric field inside a parallel plate capacitor is E. Find the amount of work done in moving a charge q over a closed loop a b c d a.Â(a) State Ampere's circuital law, expressing it in the integral form.
(b) Two long coaxial insulated solenoids, S1Â and S2Â of equal lengths are wound one over the other as shown in the figure. A steady current 'I' flow thought the inner solenoid S1Â to the other end B, which is connected to the outer solenoid S2Â through which the same current 'I' flows in the opposite direction so as to come out at end A. If n1Â and n2Â are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point
(i) Inside on the axis, andAnswer the following:
(a) Name the EM waves which are suitable for radar systems used in aircraft navigation. Write the range of frequency of these waves.
(b) If the earth did not have atmosphere, would its average surface temperature be higher or lower than what it is now? Explain.
(c) An EM wave exerts pressure on the surface on which it is incident. Justify.A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?Â
The figure given below shows the block diagram of a generalized communication system. Identify the element labelled 'X' and write its function.
For a single slit of width "a", the first minimum of the interference pattern of a monochromatic light of wavelength λ occurs at an angle of . At the same angle of  , we get a maximum for two narrow slits separated by a distance "a". Explain.Â