(a) consider a flat sheet of metal foil that is infinite in extent. it carries current, with uniform surface current density k = 200a/m i. determine a formula for the magnetic field due to this current at a distance z from the sheet [6] i. imagine that the sheet is cut to a strip m wide and infinitely long, with the current directed perpendicularly to the long axis. now it is rolled into an infinitely long cylinder of circumference 20cm a. calculate the magnetic field amplitude both inside the cylinder, and outside [4] b. derive a formula for the magnetic vector potential at a distance r from the axis of the cylinder c. briefly discuss the relative merits of the approaches using ampere's law, and using the biot-savart law to part a) of this question

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

Which of the following is a homogenous mixture? o a. a toy box filled with toys o b. blood o c. trail mix o d. spaghetti and meatballs submit

Aroll in a paper machine is powered by a separately excited dc machine. operating point 1 (under load): the roll typically operates at 764 rpm and must provide 301 nm of torque to oppose the load of the paper. the armature voltage is 230v for this operating point operating point 2 (no load): when the load is removed the speed of the roll increases to 900 rpm (the field characteristics are unchanged) la ea dev m (a) calculate the maximum torque (units of nm) that the motor can supply with this applied voltage (b) calculate the value of the armature resistance, ra (in ohms) (c) at operating point 1 (loaded condition), the field current, i, and the total input power (armature field), are measured to be to be 10 a and 28,600 w respectively. use this information to calculate the value of the field resistance, rf (in ohms). (d) (d) at operating point 1 (loaded condition), calculate the motor efficiency. express your answer as a percent to at least 2 significant digits. (d) if the field voltage is reduced by 1/2, calculate the new stall torque (in nm) of the motor (f). if the field voltage is reduced by 1/2, calculate the new no-load speed (in rad/sec)