Our monthly electricity bill contains a basic charge, which does not change with number of units used, and a charge that depends only on how many units we use. Let us say Electricity board charges Rs 110 as basic charge and charde Rs. 4 for each unit we use. If a person wants to keep his electricity bill below Rs. 250. then what should be his electricity usage

(a) What is meant by electric current ? Give its direction ? (b) Name and define its unit. (c ) Which instrument is used to measure the electric current ? How should it be connected in a circuit ?

Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by (E_(2)-E_(1)).hatn=sigma/epsi_(0) where hatn is a unit vector normal to the surface at a point and sigma is the surface charge density at that point. (The direction of hatn is from side 1 to side 2). Hence show that just outside a conductor, the electric field is (sigma hatn)/(epsi_(0)) . (b) Show that the tangetial component of electrostatic field field is continuous from one side of a charged surface to another. [Hint: For (a), use Gauss law. For (b) use the fact that work done by electrostatic field on a a closed loop is zero].

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) ?.

A manufacturer has 3 machines I, II and III installed in his factory. Machines I and II are capable of being operated for utmost 12 hours whereas machine III must be operated atleast for 5 hours a day. He produces only two items A and B each requiring the use of three machines. The number of hours required for producing 1 unit of each of the items A and B on the three machines are given below. He makes a profit of Rs 7600 on item A and Rs 400 on item B. Assume that he can sell all that he produces. (i) Formulate this as a linear programming problem. (ii) Solve the L.P.P by corner point method.

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).

"Gauss's law is true for any closed surface, no matter what its shape or size" say the following statements are true or false. a. Gauss's law implies that the total electric flux through a closed surface is zero if no charge is enclosed by the surface. b. This law is useful for the calculation of electrostatic field when the system doesn't possess any symmetry. c. In a uniform electric field, we know that the dipole experiences no net force, but experiences a torque having a relation with P and E is given by ............ where the parameters P and E have their usual meaning.

A merchant plans to sell two types of personal computers -a desktop model and a portable model that wil cost Rs. 25,000 and Rs. 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units Determine which the merchant should stock to get maximum profit merchant should stock to get maximum profit if he does not want to invest more than Rs. 70 laksh and if his profit on the dekstop model is Rs 4500 and on portable model is Rs. 5000