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E-grāmata: Problems in Classical Electromagnetism: 157 Exercises with Solutions

Andrea Macchi, Francesco Pegoraro, Giovanni Moruzzi

Formāts: EPUB+DRM
Izdošanas datums: 10-Dec-2017
Izdevniecība: Springer International Publishing AG
Valoda: eng
ISBN-13: 9783319631332

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Formāts: EPUB+DRM
Izdošanas datums: 10-Dec-2017
Izdevniecība: Springer International Publishing AG
Valoda: eng
ISBN-13: 9783319631332

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This book contains 157 problems in classical electromagnetism, most of them new and original compared to those found in other textbooks. Each problem is presented with a title in order to highlight its inspiration in different areas of physics or technology, so that the book is also a survey of historical discoveries and applications of classical electromagnetism. The solutions are complete and include detailed discussions, which take into account typical questions and mistakes by the students. Without unnecessary mathematical complexity, the problems and related discussions introduce the student to advanced concepts such as unipolar and homopolar motors, magnetic monopoles, radiation pressure, angular momentum of light, bulk and surface plasmons, radiation friction, as well as to tricky concepts and ostensible ambiguities or paradoxes related to the classical theory of the electromagnetic field. With this approach the book is both a teaching tool for undergraduates in physics, mathematics and electric engineering, and a reference for students wishing to work in optics, material science, electronics, plasma physics.

1 Basics of Electrostatics

(8)

1.1 Overlapping Charged Spheres

(1)

1.2 Charged Sphere with Internal Spherical Cavity

(1)

1.3 Energy of a Charged Sphere

(1)

1.4 Plasma Oscillations

(1)

1.5 Mie Oscillations

(1)

1.6 Coulomb explosions

(1)

1.7 Plane and Cylindrical Coulomb Explosions

(1)

1.8 Collision of two Charged Spheres

(1)

1.9 Oscillations in a Positively Charged Conducting Sphere

(1)

1.10 Interaction between a Point Charge and an Electric Dipole

(1)

1.11 Electric Field of a Charged Hemispherical Surface

(1)

2 Electrostatics of Conductors

(8)

2.1 Metal Sphere in an External Field

(1)

2.2 Electrostatic Energy with Image Charges

(1)

2.3 Fields Generated by Surface Charge Densities

(1)

2.4 A Point Charge in Front of a Conducting Sphere

(1)

2.5 Dipoles and Spheres

(1)

2.6 Coulomb's Experiment

(1)

2.7 A Solution Looking for a Problem

(1)

2.8 Electrically Connected Spheres

(1)

2.9 A Charge Inside a Conducting Shell

(1)

2.10 A Charged Wire in Front of a Cylindrical Conductor

(1)

2.11 Hemispherical Conducting Surfaces

(1)

2.12 The Force Between the Plates of a Capacitor

(1)

2.13 Electrostatic Pressure on a Conducting Sphere

(1)

2.14 Conducting Prolate Ellipsoid

(2)

3 Electrostatics of Dielectric Media

(8)

3.1 An Artificial Dielectric

(1)

3.2 Charge in Front of a Dielectric Half-Space

(1)

3.3 An Electrically Polarized Sphere

(1)

3.4 Dielectric Sphere in an External Field

(1)

3.5 Refraction of the Electric Field at a Dielectric Boundary

(1)

3.6 Contact Force between a Conducting Slab and a Dielectric Half-Space

(1)

3.7 A Conducting Sphere between two Dielectrics

(1)

3.8 Measuring the Dielectric Constant of a Liquid

(1)

3.9 A Conducting Cylinder in a Dielectric Liquid

(1)

3.10 A Dielectric Slab in Contact with a Charged Conductor

(1)

3.11 A Transversally Polarized Cylinder

(2)

Reference

(2)

4 Electric Currents

(8)

4.1 The Tolman-Stewart Experiment

(1)

4.2 Charge Relaxation in a Conducting Sphere

(1)

4.3 A Coaxial Resistor

(1)

4.4 Electrical Resistance between two Submerged Spheres (1)

(1)

4.5 Electrical Resistance between two Submerged Spheres (2)

(1)

4.6 Effects of non-uniform resistivity

(1)

4.7 Charge Decay in a Lossy Spherical Capacitor

(1)

4.8 Dielectric-Barrier Discharge

(1)

4.9 Charge Distribution in a Long Cylindrical Conductor

(1)

4.10 An Infinite Resistor Ladder

(2)

References

(2)

5 Magnetostatics

(10)

5.1 The Rowland Experiment

(1)

5.2 Pinch Effect in a Cylindrical Wire

(1)

5.3 A Magnetic Dipole in Front of a Magnetic Half-Space

(1)

5.4 Magnetic Levitation

(1)

5.5 Uniformly Magnetized Cylinder

(1)

5.6 Charged Particle in Crossed Electric and Magnetic Fields

(1)

5.7 Cylindrical Conductor with an Off-Center Cavity

(1)

5.8 Conducting Cylinder in a Magnetic Field

(1)

5.9 Rotating Cylindrical Capacitor

(1)

5.10 Magnetized Spheres

(3)

6 Magnetic Induction and Time-Varying Fields

(12)

6.1 A Square Wave Generator

(1)

6.2 A Coil Moving in an Inhomogeneous Magnetic Field

(1)

6.3 A Circuit with "Free-Falling" Parts

(1)

6.4 The Tethered Satellite

(1)

6.5 Eddy Currents in a Solenoid

(1)

6.6 Feynman's "Paradox"

(1)

6.7 Induced Electric Currents in the Ocean

(1)

6.8 A Magnetized Sphere as Unipolar Motor

(1)

6.9 Induction Heating

(1)

6.10 A Magnetized Cylinder as DC Generator

(1)

6.11 The Faraday Disk and a Self-Sustained Dynamo

(1)

6.12 Mutual Induction between Circular Loops

(1)

6.13 Mutual Induction between a Solenoid and a Loop

(1)

6.14 Skin Effect and Eddy Inductance in an Ohmic Wire

(1)

6.15 Magnetic Pressure and Pinch effect for a Surface Current

(1)

6.16 Magnetic Pressure on a Solenoid

(1)

6.17 A Homopolar Motor

(2)

References

(2)

7 Electromagnetic Oscillators and Wave Propagation

(10)

7.1 Coupled RLC Oscillators (1)

(1)

7.2 Coupled RLC Oscillators (2)

(1)

7.3 Coupled RLC Oscillators (3)

(1)

7.4 The LC Ladder Network

(1)

7.5 The CL Ladder Network

(1)

7.6 Non-Dispersive Transmission Line

(1)

7.7 An "Alternate" LC Ladder Network

(1)

7.8 Resonances in an LC Ladder Network

(1)

7.9 Cyclotron Resonances (1)

(1)

7.10 Cyclotron Resonances (2)

(1)

7.11 A Quasi-Gaussian Wave Packet

(1)

7.12 A Wave Packet along a Weakly Dispersive Line

(3)

8 Maxwell Equations and Conservation Laws

(8)

8.1 Poynting Vector(s) in an Ohmic Wire

(1)

8.2 Poynting Vector(s) in a Capacitor

(1)

8.3 Poynting's Theorem in a Solenoid

(1)

8.4 Poynting Vector in a Capacitor with Moving Plates

(1)

8.5 Radiation Pressure on a Perfect Mirror

(1)

8.6 A Gaussian Beam

(1)

8.7 Intensity and Angular Momentum of a Light Beam

(1)

8.8 Feynman's Paradox solved

(1)

8.9 Magnetic Monopoles

(2)

9 Relativistic Transformations of the Fields

(6)

9.1 The Fields of a Current-Carrying Wire

(1)

9.2 The Fields of a Plane Capacitor

(1)

9.3 The Fields of a Solenoid

(1)

9.4 The Four-Potential of a Plane Wave

(1)

9.5 The Force on a Magnetic Monopole

(1)

9.6 Reflection from a Moving Mirror

(1)

9.7 Oblique Incidence on a Moving Mirror

(1)

9.8 Pulse Modification by a Moving Mirror

(1)

9.9 Boundary Conditions on a Moving Mirror

(2)

Reference

(1)

10 Radiation Emission and Scattering

(8)

10.1 Cyclotron Radiation

(1)

10.2 Atomic Collapse

(1)

10.3 Radiative Damping of the Elastically Bound Electron

(1)

10.4 Radiation Emitted by Orbiting Charges

(1)

10.5 Spin-Down Rate and Magnetic Field of a Pulsar

(1)

10.6 A Bent Dipole Antenna

(1)

10.7 A Receiving Circular Antenna

(1)

10.8 Polarization of Scattered Radiation

(1)

10.9 Polarization Effects on Thomson Scattering

(1)

10.10 Scattering and Interference

(1)

10.11 Optical Beats Generating a "Lighthouse Effect"

(1)

10.12 Radiation Friction Force

(2)

References

(1)

11 Electromagnetic Waves in Matter

(8)

11.1 Wave Propagation in a Conductor at High and Low Frequencies

(1)

11.2 Energy Densities in a Free Electron Gas

(1)

11.3 Longitudinal Waves

(1)

11.4 Transmission and Reflection by a Thin Conducting Foil

(1)

11.5 Anti-reflection Coating

(1)

11.6 Birefringence and Waveplates

(1)

11.7 Magnetic Birefringence and Faraday Effect

(1)

11.8 Whistler Waves

(1)

11.9 Wave Propagation in a "Pair" Plasma

(1)

11.10 Surface Waves

(1)

11.11 Mie Resonance and a "Plasmonic Metamaterial"

(1)

Reference

(1)

12 Transmission Lines, Waveguides, Resonant Cavities

(8)

12.1 The Coaxial Cable

(1)

12.2 Electric Power Transmission Line

(1)

12.3 TEM and TM Modes in an "Open" Waveguide

(1)

12.4 Square and Triangular Waveguides

(1)

12.5 Waveguide Modes as an Interference Effect

(1)

12.6 Propagation in an Optical Fiber

(1)

12.7 Wave Propagation in a Filled Waveguide

100

(1)

12.8 Schumann Resonances

100

(3)

13 Additional Problems

103

(14)

13.1 Electrically and Magnetically Polarized Cylinders

103

(1)

13.2 Oscillations of a Triatomic Molecule

103

(1)

13.3 Impedance of an Infinite Ladder Network

104

(1)

13.4 Discharge of a Cylindrical Capacitor

105

(1)

13.5 Fields Generated by Spatially Periodic Surface Sources

105

(1)

13.6 Energy and Momentum Flow Close to a Perfect Mirror

106

(1)

13.7 Laser Cooling of a Mirror

106

(1)

13.8 Radiation Pressure on a Thin Foil

107

(1)

13.9 Thomson Scattering in the Presence of a Magnetic Field

107

(1)

13.10 Undulator Radiation

108

(1)

13.11 Electromagnetic Torque on a Conducting Sphere

108

(1)

13.12 Surface Waves in a Thin Foil

109

(1)

13.13 The Fizeau Effect

109

(1)

13.14 Lorentz Transformations for Longitudinal Waves

110

(1)

13.15 Lorentz Transformations for a Transmission Cable

110

(1)

13.16 A Waveguide with a Moving End

111

(1)

13.17 A "Relativistically" Strong Electromagnetic Wave

111

(1)

13.18 Electric Current in a Solenoid

112

(1)

13.19 An Optomechanical Cavity

113

(1)

13.20 Radiation Pressure on an Absorbing Medium

113

(1)

13.21 Scattering from a Perfectly Conducting Sphere

114

(1)

13.22 Radiation and Scattering from a Linear Molecule

114

(1)

13.23 Radiation Drag Force

115

(2)

Reference

115

(2)

S-1 Solutions for
Chapter 1

117

(20)

S-1.1 Overlapping Charged Spheres

117

(1)

S-1.2 Charged Sphere with Internal Spherical Cavity

118

(1)

S-1.3 Energy of a Charged Sphere

119

(2)

S-1.4 Plasma Oscillations

121

(1)

S-1.5 Mie Oscillations

122

(2)

S-1.6 Coulomb Explosions

124

(3)

S-1.7 Plane and Cylindrical Coulomb Explosions

127

(3)

S-1.8 Collision of two Charged Spheres

130

(1)

S-1.9 Oscillations in a Positively Charged Conducting Sphere

131

(1)

S-1.10 Interaction between a Point Charge and an Electric Dipole

132

(2)

S-1.11 Electric Field of a Charged Hemispherical surface

134

(3)

S-2 Solutions for
Chapter 2

137

(32)

S-2.1 Metal Sphere in an External Field

137

(1)

S-2.2 Electrostatic Energy with Image Charges

138

(4)

S-2.3 Fields Generated by Surface Charge Densities

142

(2)

S-2.4 A Point Charge in Front of a Conducting Sphere

144

(2)

S-2.5 Dipoles and Spheres

146

(2)

S-2.6 Coulomb's Experiment

148

(3)

S-2.7 A Solution Looking for a Problem

151

(2)

S-2.8 Electrically Connected Spheres

153

(1)

S-2.9 A Charge Inside a Conducting Shell

154

(1)

S-2.10 A Charged Wire in Front of a Cylindrical Conductor

155

(4)

S-2.11 Hemispherical Conducting Surfaces

159

(1)

S-2.12 The Force between the Plates of a Capacitor

160

(2)

S-2.13 Electrostatic Pressure on a Conducting Sphere

162

(2)

S-2.14 Conducting Prolate Ellipsoid

164

(5)

S-3 Solutions for
Chapter 3

169

(24)

S-3.1 An Artificial Dielectric

169

(1)

S-3.2 Charge in Front of a Dielectric Half-Space

170

(2)

S-3.3 An Electrically Polarized Sphere

172

(1)

S-3.4 Dielectric Sphere in an External Field

173

(2)

S-3.5 Refraction of the Electric Field at a Dielectric Boundary

175

(2)

S-3.6 Contact Force between a Conducting Slab and a Dielectric Half-Space

177

(4)

S-3.7 A Conducting Sphere between two Dielectrics

181

(3)

S-3.8 Measuring the Dielectric Constant of a Liquid

184

(1)

S-3.9 A Conducting Cylinder in a Dielectric Liquid

185

(2)

S-3.10 A Dielectric Slab in Contact with a Charged Conductor

187

(2)

S-3.11 A Transversally Polarized Cylinder

189

(4)

S-4 Solutions for
Chapter 4

193

(18)

S-4.1 The Tolman-Stewart Experiment

193

(1)

S-4.2 Charge Relaxation in a Conducting Sphere

194

(2)

S-4.3 A Coaxial Resistor

196

(2)

S-4.4 Electrical Resistance between two Submerged Spheres (1)

198

(1)

S-4.5 Electrical Resistance between two Submerged Spheres (2)

199

(2)

S-4.6 Effects of non-uniform resistivity

201

(1)

S-4.7 Charge Decay in a Lossy Spherical Capacitor

202

(2)

S-4.8 Dielectric-Barrier Discharge

204

(1)

S-4.9 Charge Distribution in a Long Cylindrical Conductor

205

(4)

S-4.10 An Infinite Resistor Ladder

209

(2)

S-5 Solutions for
Chapter 5

211

(18)

S-5.1 The Rowland Experiment

211

(1)

S-5.2 Pinch Effect in a Cylindrical Wire

212

(2)

S-5.3 A Magnetic Dipole in Front of a Magnetic Half-Space

214

(3)

S-5.4 Magnetic Levitation

217

(2)

S-5.5 Uniformly Magnetized Cylinder

219

(1)

S-5.6 Charged Particle in Crossed Electric and Magnetic Fields

220

(2)

S-5.7 Cylindrical Conductor with an Off-Center Cavity

222

(1)

S-5.8 Conducting Cylinder in a Magnetic Field

223

(1)

S-5.9 Rotating Cylindrical Capacitor

224

(1)

S-5.10 Magnetized Spheres

225

(4)

S-6 Solutions for
Chapter 6

229

(44)

S-6.1 A Square Wave Generator

229

(2)

S-6.2 A Coil Moving in an Inhomogeneous Magnetic Field

231

(1)

S-6.3 A Circuit with "Free-Falling" Parts

232

(2)

S-6.4 The Tethered Satellite

234

(2)

S-6.5 Eddy Currents in a Solenoid

236

(3)

S-6.6 Feynman's "Paradox"

239

(3)

S-6.7 Induced Electric Currents in the Ocean

242

(1)

S-6.8 A Magnetized Sphere as Unipolar Motor

243

(3)

S-6.9 Induction Heating

246

(3)

S-6.10 A Magnetized Cylinder as DC Generator

249

(2)

S-6.11 The Faraday Disk and a Self-sustained Dynamo

251

(2)

S-6.12 Mutual Induction Between Circular Loops

253

(1)

S-6.13 Mutual Induction between a Solenoid and a Loop

254

(1)

S-6.14 Skin Effect and Eddy Inductance in an Ohmic Wire

255

(6)

S-6.15 Magnetic Pressure and Pinch Effect for a Surface Current

261

(3)

S-6.16 Magnetic Pressure on a Solenoid

264

(2)

S-6.17 A Homopolar Motor

266

(7)

S-7 Solutions for
Chapter 7

273

(26)

S-7.1 Coupled RLC Oscillators (1)

273

(3)

S-7.2 Coupled RLC Oscillators (2)

276

(1)

S-7.3 Coupled RLC Oscillators (3)

276

(3)

S-7.4 The LC Ladder Network

279

(3)

S-7.5 The CL Ladder Network

282

(1)

S-7.6 A non-dispersive transmission line

283

(2)

S-7.7 An "Alternate" LC Ladder Network

285

(3)

S-7.8 Resonances in an LC Ladder Network

288

(2)

S-7.9 Cyclotron Resonances (1)

290

(3)

S-7.10 Cyclotron Resonances (2)

293

(2)

S-7.11 A Quasi-Gaussian Wave Packet

295

(1)

S-7.12 A Wave Packet Traveling along a Weakly Dispersive Line

296

(3)

S-8 Solutions for
Chapter 8

299

(20)

S-8.1 Poynting Vector(s) in an Ohmic Wire

299

(2)

S-8.2 Poynting Vector(s) in a Capacitor

301

(1)

S-8.3 Poynting's Theorem in a Solenoid

302

(1)

S-8.4 Poynting Vector in a Capacitor with Moving Plates

303

(4)

S-8.5 Radiation Pressure on a Perfect Mirror

307

(3)

S-8.6 Poynting Vector for a Gaussian Light Beam

310

(2)

S-8.7 Intensity and Angular Momentum of a Light Beam

312

(2)

S-8.8 Feynman's Paradox solved

314

(2)

S-8.9 Magnetic Monopoles

316

(3)

S-9 Solutions for
Chapter 9

319

(20)

S-9.1 The Fields of a Current-Carrying Wire

319

(4)

S-9.2 The Fields of a Plane Capacitor

323

(1)

S-9.3 The Fields of a Solenoid

324

(1)

S-9.4 The Four-Potential of a Plane Wave

325

(2)

S-9.5 The Force on a Magnetic Monopole

327

(1)

S-9.6 Reflection from a Moving Mirror

328

(4)

S-9.7 Oblique Incidence on a Moving Mirror

332

(1)

S-9.8 Pulse Modification by a Moving Mirror

333

(2)

S-9.9 Boundary Conditions on a Moving Mirror

335

(4)

S-10 Solutions for
Chapter 10

339

(22)

S-10.1 Cyclotron Radiation

339

(3)

S-10.2 Atomic Collapse

342

(1)

S-10.3 Radiative Damping of the Elastically Bound Electron

343

(2)

S-10.4 Radiation Emitted by Orbiting Charges

345

(2)

S-10.5 Spin-Down Rate and Magnetic Field of a Pulsar

347

(1)

S-10.6 A Bent Dipole Antenna

348

(1)

S-10.7 A Receiving Circular Antenna

349

(2)

S-10.8 Polarization of Scattered Radiation

351

(1)

S-10.9 Polarization Effects on Thomson Scattering

352

(3)

S-10.10 Scattering and Interference

355

(1)

S-10.11 Optical Beats Generating a "Lighthouse Effect"

356

(1)

S-10.12 Radiation Friction Force

357

(4)

S-11 Solutions for
Chapter 11

361

(20)

S-11.1 Wave Propagation in a Conductor at High and Low Frequencies

361

(2)

S-11.2 Energy Densities in a Free Electron Gas

363

(2)

S-11.3 Longitudinal Waves

365

(2)

S-11.4 Transmission and Reflection by a Thin Conducting Foil

367

(2)

S-11.5 Anti-Reflection Coating

369

(1)

S-11.6 Birefringence and Waveplates

370

(1)

S-11.7 Magnetic Birefringence and Faraday Effect

371

(3)

S-11.8 Whistler Waves

374

(1)

S-11.9 Wave Propagation in a "Pair" Plasma

375

(1)

S-11.10 Surface Waves

376

(1)

S-11.11 Mie Resonance and a "Plasmonic Metamaterial"

377

(4)

S-12 Solutions for
Chapter 12

381

(16)

S-12.1 The Coaxial Cable

381

(3)

S-12.2 Electric Power Transmission Line

384

(1)

S-12.3 TEM and TM Modes in an "Open" Waveguide

385

(2)

S-12.4 Square and Triangular Waveguides

387

(2)

S-12.5 Waveguide Modes as an Interference Effect

389

(2)

S-12.6 Propagation in an Optical Fiber

391

(2)

S-12.7 Wave Propagation in a Filled Waveguide

393

(1)

S-12.8 Schumann Resonances

394

(3)

References

395

(2)

S-13 Solutions for
Chapter 13

397

(48)

S-13.1 Electrically and Magnetically Polarized Cylinders

397

(4)

S-13.2 Oscillations of a Triatomic Molecule

401

(1)

S-13.3 Impedance of an Infinite Ladder Network

402

(3)

S-13.4 Discharge of a Cylindrical Capacitor

405

(3)

S-13.5 Fields Generated by Spatially Periodic Surface Sources

408

(3)

S-13.6 Energy and Momentum Flow Close to a Perfect Mirror

411

(2)

S-13.7 Laser Cooling of a Mirror

413

(1)

S-13.8 Radiation Pressure on a Thin Foil

414

(3)

S-13.9 Thomson Scattering in the Presence of a Magnetic Field

417

(1)

S-13.10 Undulator Radiation

417

(2)

S-13.11 Electromagnetic Torque on a Conducting Sphere

419

(2)

S-13.12 Surface Waves in a Thin Foil

421

(2)

S-13.13 The Fizeau Effect

423

(2)

S-13.14 Lorentz Transformations for Longitudinal Waves

425

(1)

S-13.15 Lorentz Transformations for a Transmission Cable

426

(3)

S-13.16 A Waveguide with a Moving End

429

(2)

S-13.17 A "Relativistically" Strong Electromagnetic Wave

431

(2)

S-13.18 Electric Current in a Solenoid

433

(1)

S-13.19 An Optomechanical Cavity

434

(2)

S-13.20 Radiation Pressure on an Absorbing Medium

436

(2)

S-13.21 Scattering from a Perfectly Conducting Sphere

438

(1)

S-13.22 Radiation and Scattering from a Linear Molecule

439

(3)

S-13.23 Radiation Drag Force

442

(3)

References

443

(2)

Appendix A Some Useful Vector Formulas

445

(4)

Index

449

Andrea Macchi is a research scientist at CNR/INO, Pisa, Italy, and lecturer of classical electromagnetism and of plasma physics at the Physics Department of the University of Pisa. His research interests include superintense laser-matter interactions, laser-driven acceleration of particles, high field plasmonics, nonlinear plasma dynamics. He has published about 80 papers on peer reviewed journals and the textbook "A Superintense Laser-Plasma Interaction Primer" (Springer, 2013). Giovanni Moruzzi is a retired associated professor from the Physics Department of the University of Pisa, where he is still teaching classical electromagnetism. His research interests cover atomic and molecular spectroscopy, in particular the assignment of dense molecular spectra involving internal torsional rotation. He has published more than 70 papers on peer-reviewed journals and has been coeditor and coauthor of two scientific books.

Francesco Pegoraro is a full professor at the Physics Department of the University of Pisa where he teaches classical electromagnetism and plasma physics and a corresponding member of the "Accademia dei Lincei'' in Rome. His research interests cover different areas of theoretical plasma physics ranging from magnetically confined plasmas, space and astrophysical plasmas to laser produced relativistic plasmas. He has published some 300 research papers on peer reviewed journals.

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E-grāmata: Problems in Classical Electromagnetism: 157 Exercises with Solutions

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