A pole has to be erected at a point on the boundary of a circular ground of diameter 20m in such a way that the difference of its distance form two diameterically opposite fixed gates P and Q on the boundary is 4 m. Is it possible to do so? If answer is yes at what distance from the two gates should the pole be erected?

The upper 3/4 th portion of a vertical pole subtends an angle theta such that tan theta=3/5 at a point in the horizontal plane through its foot and at a distance 40m from the foot. Find the possible height of the vertical pole.

Suppose the Government has decided to erect a new Electrical Power Transmission Substation to provide better power supply to two villages namely A and B . The substation has to be on the line l. The distances of villages A and B from the foot of the perpendiculars P and Q on the line l are B from the foot of the perpendiculars P and Q on the line l are 3 km and 5 km respectively and the distance between P and Q is 6 km. (i) What is the smallest length of cable required to connect the two villages. (ii) Find the equations of the cable lines that connect the power station to two villages.(Using the knowledge in conjunction with the principle of reflection allows for approach to solve this problem) .

A telescope has an objective of diameter 60 cm.The focal lengths of the objective and eyepiece are 2.0 m and 1.0 cm respectively. The telescope is directed to view two distant almost point sources of light, (e.g., two stars of a binary) The sources are roughly at the same distance = ( =10^4 light year) along the line of sight but are separated transverse to the line of sight by a distance of 10^10 m. Will the telescope resolve the two objects i.e. will it see two distant stars?

a. The top of the atmosphere is at about 400 kV with respectto the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 Vm^(-1). Why then do we not get a electric shock as we step out of our house into the openy (Assume the house to be a steel cage so there is no field inside!) b. A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area 1m^(2) . Will he get an electric shock if he touches the metal sheet next morning? c. The discharging current in the atmosphere due to the small conductivity of air is known to be 1800A on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged? d. What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (Hint: The earth has an electric field of about 100 Vm^(-1) at its surface in the downward direction, corresponding to a surface charge density =-10^(-9) Cm^(-2) ?.

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate does it change appreciably ? b. The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism why ? c. The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism . What might be the ' battery ' (i.e., the source of energy) to sustain these currents ? d. The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past ? e. The earth's field departs from its dipole substantially at large distances (greater than about 30,000 km) what agencies may be responsible for this distortion ? f. Interstellar space has an extremely weak magnetic field of the order of 10^(-12) T, Can such a weak field be of any significant consequence ? Explain. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]

Two large conducting spheres carrying charges Q_1, and Q_2, are brought close to each other. Is the magnitude of electrostatic force between theme exactly given by (Q_1Q_2)/(4pi epsi_(0) r^(2)) , where r is the distance between their centres? b. If Coulomb's law involved 1/r^(3) dependence ("instead of "1/r^2), would Gauss law be still true? c. A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? d. What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? e. We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? f. What meaning would you give to the capacitance of a single conductor? g. Guess a possible reason why water has a much greater dielectric constant (=80) than say, mica (= 6).

Two parallel towers A and B of different heights are at some distance on same level ground. If angle of elevation of a point P at 20 m height on tower B from a point Q at 10 m height on tower A is theta and is equal to half the-angle of elevation of point R at 50 m height on A from point P on B , then sine of theta is

Let AP and BQ be two vertical poles at points A and B, respectively. If AP = 16 m, BQ = 22 m and AB = 20 m, then find the distance of a point R on AB from the point A such that RP^(2) + RQ^(2) is minimum.