Question

1. adapted from Prob. 5, p. 298-299, Brown's Introductory Physics II) Consider the second diagram on p. 298. The solenoid has N turns, length / (L in the figure, which you might have confused with the self-inductance), and radius (A in the figure, which you might have confused with the area). The voltage of the battery is V, (v in the figure, which you might have confused with a velocity) (a) Find the self-inductance L of the solenoid in terms of N, r, and I (b) If the wire that the solenoid is made of has radius a and resistivity p, find its resistance R in terms of N, p, rand a (Hint: this is a throwback to Chapter 5.) e) Starting with Kirchhoff's loop rule and what we know about the emf (üie. the voltage) induced in a solenoid by a changing current in that solenoid, find an expression for the derivative of the current di dt in terms of the inductance and resistance of the sol Note: the solenoid is acting as both an inductor (as in (a)) and a resistor (as in (b) so there should be both an Ohm's Law voltage and a Faraday's Law voltage appearing in your loop rule. a) Using your expresson from (o (which sa differential equation of the form that we have seem several times this semester), use your handy differential equation guide to find the current i(t) in the circuit assuming that the switch S is closed at time0. Draw a qualitative plot of i(). What value does the current approach at very large times?

Answer 1