Acoil of 40 turns is wrapped around a long solenoid of cross-sectional area 7.5×10−3m2. the solenoid is 0.50 m long and has 500 turns. (a) what is the mutual inductance of this system? (b) the outer coil is replaced by a coil of 40 turns whose radius is three times that of the solenoid. what is the mutual inductance of this configuration?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit