A current I (t) = 10 sin (wt) ows through a long solenoid with n turns per meter and diameter d, Where I 0 is the current amplitude and w is the angular frequency. Derive an expression for the magnitude of the induced electric eld Ein (r, t) inside the solenoid as a function of the distance r from the solenoid's central axis and the time I. Your expression may include the variables I 0, a), d, n, and the permeability of free space M0~ Em (r,t) = %,Lton10w(cos(wt))(r) Derive an expression for the magnitude of the induced electric eld Eout (r, t) outside the solenoid as a function of r and t. Your expression may include the variables 10, a), d, n, and [40. %(,u0n10a)(cos(a)t) ) %) Incorrect Mindy, a medical device engineer, is designing an apparatus to monitor the breathing of a patient. The apparatus consists of a stretchable loop of conductive material wrapped in a small band around the patient's chest. A constant uniform external magnetic eld is produced by a nearby solenoid. As the patient inhales, his chest expands, stretching the chest band. The resulting increase in the area of the loop causes an emf to be induced in the loop. By measuring the induced emf, a device user can estimate the patient's breathing rate. Mindy needs the apparatus to be able to detect a change in area as small as 3.50 cm2 occuring over a time period of 1.50 s. If the minimum emf that can be reliably detected is 2.00 x 104 V, What is the magnitude of the minimum external magnetic eld that would be needed from the solenoid? magnitude of minimum external magnetic eld: 0-86 T Due to practical constraints, the largest magnetic eld that the solenoid can actually produce is 2.40 X 103 T. Mindy decides to compensate by using multiple loops of the conductive material in series. How many conductive loops should be in the chest band? 356 minimum number of conductive loops: Incorrect A sinusoidally oscillating current I (t) with an amplitude of 8.55 A and a frequency of 671 cycles per second is carried by a long, straight wire. A rectangular loop of copper wire with dimensions b = 63.2 cm by c = 28.4 cm is located a = 70.2 cm from the straight wire, and is coplanar with it. Calculate the average power Pavg dissipated by the loop if its resistance is 34.3 Q. [(t)