223

Chapter 26

A capacitor is a device that one can use to store an electric potential energy.

(Spring: mechanical potential energy) Useful in electronics and

microelectronics

224

(C: capacitance SI: farad)

225

226

The plates of a parallel-plate capacitor are separated by a distance d=1.0mm. What must be the plate area if the capacitance is to be 1.0F? Sol:

0εCdA = = 1.1X108 m2 (large!)

227

228

229

230

231

Energy density μ: The potential energy per unit volume

232

What is the potential energy of the two-capacitor system in problem 26-4 before and after switch S is closed.

Ui= JVC μ4.7021 2

01 =

Uf= JVCVC μ0.2021

21 2

22

1 =+ (smaller!)

Heat

(c) What is the radius R0 of an imaginary spherical surface such that half of the stored potential energy

lies within it?

(a)

233

(b)

(c) ∫∫∞

=R

R

RdUdU

210

20

2

2

8

))(4)((

rdrqdU

drrudU

πε

π

=

=

∫∫∞

=R

R

R rdr

rdr

22 210

RRR 20

111=−

=R0=13.7cm R

κ : a numerical factor

234

Water,etc.

235

236

237

(a)

(b)

(c)

(d)

(e)

238

(f)

Exercises:17,29,41

239

Chapter 27

Electric currents: Charges in motion

240

Current is a scalar. For historical reasons, a current arrow is drawn in the direction in which positive charge carriers would move, even if the actual charge carriers are negative and move in the opposite direction.

For a constant current

(SI unit: A/m2)

Electrons tend to drift with a drift speed νd in the direction opposite to the

current.

241

(a) Uniform current density

242

(b)

One end of an aluminum wire whose diameter is 2.5mm is welded to one end of a copper wire whose diameter is1.8mm. The composite wire carries a steady current I of 17ma. (a) What is the current density in each wire? (b) What is the drift speed of the conduction electrons in the copper wire? Assume that, on the average,

each copper atom contributes one conduction electron.

(a) Jcu=2)

2(

17dmA

π=6.7X103 A/m2

12311 /105.3 A

cu

A

cu

A JmAXAA

JJ

=⇒=

(b)

243

hmmsmXX

MN

mAXA

d /8.1/109.4)1060.1)((

/107.6 7

19

23

=== −

−ρν

Consider a strip of silicon has a rectangular cross section with width w=3.2mm and height h=250μm, and through which there is a uniform current I of 5.2ma. The silicon is an n-type semiconductor, having been “doped” with a controlled phosphorus impurity. N=1.5X1023m-3 (a) What is the current density in the strip? Sol: J=i/wh=6500A/m2

(b) What is the drift speed? Sol: vd=J/ne=27cm/s

R: resistance

244

ρ: resistivity

245

246

( pn junction)

or

If an electron of mass m is placed in an electric field of magnitude E,

On the average

( : the mean free time)

247

(a)

(b)

248

A wire of length L=2.35m and diameter d=1.63mm carries a current I of 1.24A. The wire dissipates electrical energy at the rate P of 48.5mW. of what is the wire made? Sol:

P= 2

24d

Liπρ ρ=2.80x10-8Ω．M Al

The valence band: the highest band that is occupied by electrons. Superconductors: Hg ,..... High temperature superconductivity : Paul chu,...

Exercises:25,31,41

249

Chapter 28

A “charge pump”: a device that by doing work on the charge carriers maintains a potential difference between a pair of terminals.

an emf device (electromotive force) Def

dqdW

=ξ

Ideal emf device: no internal resistance Real emf device: (Battery) has internal resistance to the internal movement of charge

250

251

252

(Kirchhoff’s current law)

253

254

(a)

255

(b)

(c)

256

Q=CV

Def. τ= RC : (the time constant )

t=τ

257

K=?

Initial condition

A capacitor of capacitance C is discharging through a resistor of resistance R

(a)In terms of the time constant τ=RC, when will the charge on the capacitor be half its

initial value?

258

(b)When will the energy stored in the capacitor half its initial value?

(c)At what rate PR is thermal energy produced in the resistor during the discharging process?

At what rate Pc is stored energy lost by the capacitor during the charging process

(a)

RCte

eqq

eqq

RCt

RCt

RCt

−==

=

=

−

−

−

)ln(21ln

21

00

0

T=-ln(1/2)(RC)=0.69τ

(b)

U= RCt

RCt

eUeC

qC

q 2

0

220

2

22−−

==

RCt

eUU2

0021 −

=

ln(1/2)=-2t/RC t=0.35τ

(c)

PR=i2R= ReRCq RC

t20 ][

−

= RCt

eRCq 2

2

20 −

Pc=dU/dt= RCt

RCt

RCt

eRCq

eRCU

eUdtd 2

2

20

20

2

022

)(−−−

−=−=

PR+PC=0

Exercises:31,43

259

Chapter 29

A charged plastic rod produces a vector field – the electric field E in the space around it. A magnet produces a vector field – the magnetic field B in the space around it. Setting up magnetic fields

(1) Moving electrically charged particles, such as a current in a wire (2) Elementary particles such as electrons have an intrinsic magnetic field around

them. Def.

--Using the right hand rule.

SI unit: Tesla (T)

260

261

(small) a=?

(large) (K<<mc2) relativistic

262

We have

263

Hall potential difference

264

265

266

267

Copper: screens the electric field.

(a) relativity (b) large r

In vector form:

268

Figure 29-21 shows a length of wire with a central semicircular arc, placed in a uniform magnetic field b that points out of the plane of the figure. If the wire carries a current i , what resultant force F acts on it?

269

2

0

1 0 3 θ

R

dF

dL

dFsinθ

Sol: F1=F3=iLB

dF=iBdL=iB(Rdθ)

iBRdiBRiBRddFF 2sinsin)(sin0002 ==== ∫∫∫ θθθθθπππ

F= F1+ F2+F3 =2iB(L+R)

Electric motor

270

Right-hand rule

271

Def

(magnetic dipole)

ΔU=(+μB)-(- μB)=2μB

Exercises:19,35,41,55