You are given a length (l) of wire that has radius (a)and are told to wind it into an inductor in the shape of a helix that has a circular cross section of radius (r). the windings are to be as close together as possible without overlapping. show that the self-inductance of this inductor is l = 1/4nrl/a.

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?

Can you match these to the correct definition

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.