91Ó°ÊÓ

The switch in FIGURE P30.77 has been open for a long time. It is closed at $t=0\mathrm{s}$.

a. After the switch has been closed for a long time, what is the current in the circuit? Call this current $I_0$.

b. Find an expression for the current $I$as a function of time. Write your expression in terms of $I_{0,},R,\text{and}L$.

c. Sketch a current-versus-time graph from $t=0\mathrm{s}$until the current is no longer changing.

The earth's magnetic field strength is$5.0×{10}^{−5}\text{T}$ . How fast would you have to drive your car to create a $1.0\text{V}$motional emf along your $1.0−\text{m}$-tall radio antenna? Assume that the motion of the antenna is perpendicular to$\stackrel{→}{B}$ .

What is the direction of the induced current in FIGURE Q$30.1$

A solenoid is wound as shown in FIGURE EX30.10.

a. Is there an induced current as magnet 1 is moved away from the solenoid? If so, what is the current direction through resistor R ?

b. Is there an induced current as magnet 2 is moved away from the solenoid? If so, what is the current direction through resistor R?

10. An inductor with a$2.0\text{A}$ current stores energy. At what current will the stored energy be twice as large?

I

I The metal equilateral triangle in FIGURE EX$30.11,20\mathrm{cm}$on each side, is halfway into a$0.10\mathrm{T}$magnetic field.

a. What is the magnetic flux through the triangle?

b. If the magnetic field strength decreases, what is the direction of the induced current in the triangle?

11. a. Can you tell which of the inductors in FIGURE Q30.11 has the larger current through it? If so, which one? Explain.

b. Can you tell through which inductor the current is changing more rapidly? If so, which one? Explain.

c. If the current enters the inductor from the bottom, can you tell if the current is increasing, decreasing, or staying the same? If so, which? Explain.

FIGURE Q30.11

The current in the solenoid of FIGURE EX30.12 is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop? If so, is the loop current cw or ccw?

The loop in FIGURE EX30.13 is being pushed into the magnetic field at . The resistance of the loop is$0.10\mathrm{Î\copyright }$. What are the direction and the magnitude of the current in the loop?

13. Rank in order, from largest to smallest, the three time constants ${\mathrm{Ï„}}_{\text{a}}$to ${\mathrm{Ï„}}_{\text{c}}$for the three circuits in FIGURE Q30.13. Explain.