For the given statements identify the necessary and sufficent conditions.
t: If you drive over 80km per hour, then you will get a fine.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.

Rewrite each of the following statements in the form ''p if and only if q'' q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Write each of the following statements in the form ''if-then'' To get an A^(+) in the class, it is necessary that you do all the exercises of the book.

Write each of the following statements in the form "if-then" i. You get a job implies that your credentials are good. ii. The bannana trees will bloom if it stays warm for a month. iii. A quadrilateral is a parallelogram if its diagonals bisect each other. iv. to get an A^(+) in the class, it is necessary that you do all the exercises of the book.

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.]

You are given a solenoid of length 'l', number of turns per unit length 'n' and area of cross-section A. When a current 'I' passes through it, a. What is the total magnetic flux through the solenoid? b. What is the self inductance of the solenoid? c. How does the value of self inductance get affected if some material of high relative permeability is filled inside the solenoid?