Chapter 30: Electromagnetic Induction

Experiments to study vision often need to track the movements BI0 of a subject's eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses with a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider the experiment of FIGURE P30.60 in which a 20 -turn, 6.0-mm-diameter coil of wire circles the subject's cornea while a 1.0 T magnetic field is directed as shown. The subject begins by looking straight ahead. What $\text{emf}$is induced in the coil if the subject shifts his gaze by $5^{\circ }\text{in}0.20\mathrm{s}?$

A 10-turn coil of wire having a diameter of 1.0 cm and a resistance of $0.20\mathrm{\Omega }$is in a $1.0\mathrm{mT}$ magnetic field, with the coil oriented for maximum flux. The coil is connected to an uncharged $1.0\mu \mathrm{F}$ capacitor rather than to a current meter. The coil is quickly pulled out of the magnetic field. Afterward, what is the voltage across the capacitor?

Equation 30.26 is an expression for the induced electric field CALC inside a solenoid$(r<R)$ . Find an expression for the induced electric field outside a solenoid$(r>R)$ in which the magnetic field is changing at the rate$dB/dt$ .

64. II A solenoid inductor has an emf of $0.20\text{V}$when the current through it changes at the rate $10.0\text{A}/\text{s}$ . A steady current of 0.10 A produces a flux of $5.0\mu \text{Wb}$per turn. How many turns does the inductor have?

One possible concern with MRI (see Exercise 28) is turning the magnetic field on or off too quickly. Bodily fluids are conductors, and a changing magnetic field could cause electric currents to flow through the patient. Suppose a typical patient has a maximum cross section area of $0.060{\mathrm{m}}^2$. What is the smallest time interval in which a $5.0\mathrm{T}$magnetic field can be turned on or off if the induced $\text{emf}$around the patient's body must be kept to less than $0.10\mathrm{V}?$?

66. II FIGURE P30.66 shows the current through a$10\text{mH}$ inductor. Draw a graph showing the potential difference$\Delta V_{\text{L}}$ across the inductor for these$6\text{ms}$ .

67. II FIGURE P30.67 shows the potential difference across a potential difference across a $50\text{mH}$inductor. The current through the inductor at $t=0\text{s}$is $0.20\text{A}$. Draw a graph showing the current through the inductor from $t=0\text{s}$to $t=40\text{ms}$

68. II A inductor with negligible resistance has a 1.0 A current through it. The current starts to increase at $t=0\text{s}$, creating a constant $5.0\text{mV}$voltage across the inductor. How much charge passes through the inductor between $5.0\text{mV}$and $t=5.0\text{s}$?

69. II The current through inductance $L$is given by$I=I_0\sin \omega t$ .

CALC a. Find an expression for the potential difference$\Delta V_{\text{L}}$ across the inductor.

b. The maximum voltage across the inductor is $0.20\text{V}$when $L=50\mu \text{H}$and $f=500\text{kHz}$. What is$I_0$ ?

A bar magnet is pushed toward a loop of wire as shown in FIGURE Q30.7. Is there a current in the loop? If so, in which direction? If not, why not?