In field and wave electromagnetics 2nd edition (david k cheng) problem 6-6
figure 6-37 shows an infinitely long solenoid with air core having a radius b and n closely wound turns per unit length. the windings are slanted at an angle α and carry a curren i. determine the magnetic flux density both inside and outside the solenoid.
in solution this problem can be divided two small problems. magnetic flux density due to surface of the cylindrical tube b1
and magnetic flux density due to solenoid coil b2 and solution say surface current is 2πbnisinα.
but i cant understand why surface current is 2πbnisinα. why solenoid length l is ignored?

Order the sequence of ideas that lead to marie curies discovery of radioactive elements number the events in chronological order starting with the oldest

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Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?