PDF 學年上學期高二物理

102學年上學期高二物理 黃信健.

高二物理 3 高斯定律.

3 Gauss’ Law. How wide is a lightning strike ?.



3-1 A New Look at Coulomb’s Law •Using Gauss’s law to take advantage of special symmetry situations •Gaussian surfaces •高斯面上各點電場與面 內總電荷相關.  0  qenc.

3-2 Flux (通量/流量) •For a fluid. m/s × m2 = m3/s.     (v cos  ) A  vAcos   v  A.



Basking shark 姥鯊.

3-3 Flux of an Electric Field •For a flat surface.     ( E cos ) A  EA cos  E  A •For a arbitrary (asymmetric) surface.        E   A   E  dA.

•An arbitrary Gaussian surface.

Ex.3-1 A cylindrical Gaussian surface.      E  dA         E  dA   E  dA   E  dA a. b.   EA  0  EA  0. c.

Ex.3-2 A nonuniform electric field and a Gaussian cube E  3.0 xiˆ  4.0 ˆj dA  dAiˆ r  . E  dA . ˆ  4.0 ˆj )  ( dAiˆ) (3.0 xi .

Ex.3-2 right face r .  E  dA.   (3.0 xiˆ  4.0 ˆj )  ( dAiˆ)   [(3.0 x )( dA)iˆ  iˆ  (4.0)( dA) ˆj  iˆ)   (3.0 xdA  0)  3.0  xdA  3.0  3.0dA  9.0  dA  36 N  m / C 2.

Ex.3-2 left and top faces left face: dA  dAiˆ  l  3.0 1.0dA  3.0 dA  12 N  m / C 2.  t   (3.0 xiˆ  4.0 ˆj )  ( dAjˆ)   [(3.0 x )( dA)iˆ  ˆj  (4.0)( dA)( ˆj  ˆj )]   (0  4.0dA)  4.0  dA  16 N  m / C 2.

3-4 Gauss’ Law •Flux  enclosed charge.  0.     0  E  dA  qenc.

Ex.3-3 bottom, front and back  b  16 N  m / C ,  f   b  0 2.  t  24 N  m / C 2. qenc   0  t  (8.85  10  2.110. 12. 10. C. C / N  m )(24 N  m / C ) 2. 2. 2.

3-5 Gauss’ Law and Coulomb’ Law •From G.L. to C.L..    0  E  dA   0  EdA  q.  0 E  dA  q  0 E ( 4r )  q 2. 1. q E 2 4 0 r.

3-6 A Charged Isolated Conductor • 同號電荷相斥   • 導體內部無電場  0 E  dA  qenc. .

Human nerve cell.

Van de Graaff electrostatic generator.

ES shielding–Faraday Cage.

The external electric field. qenc  A,   EA.   0 EA  A  E  0.

3-7 Applying Gauss’ Law: Cylindrical Symmetry qenc  h, A = 2rh.  0 E 2rh  h  E  2 0 r.

Ex.3-4 A lightning strike  r 2 0 E 3. 1  10  6 2 0 (3  10 )  6m.

3-8 Applying Gauss’ Law: Planar Symmetry.   E  dA  EdA.   0 ( EA  EA)  A  E  2 0.

•Two Conducting Plates 1 E 0. E . 2 1. 0.   0.

ex.3-5 Two‖nonconducting sheets.  E  2 0.  E  2 0.

3-9 Applying Gauss’ Law: Spherical Symmetry •The Shell Theorems. 1. q E (r  R) 2 4 0 r E 0. (r  R).

A spherically symmetric charge distribution –ρ (r). q E ( r  R) 2 4 0 r 1.

Uniform distribution 4 3  r 3 q 3 r   q  q 3 q 4 R 3 R 3 1 q q E ( )r 2 3 4 0 r 4 0 R.

Ex.3-6 The electric field vs. r. 17. q  Ze  (79)e  1.264  10 C 1 q 21 E = 3.0  10 N / C 2 4 0 r.

3-10 Gauss’ Law in Differential Form  0   0  E  dA  qenc .  E  dA . . E  dA . S. qenc.  0 Divergence Theorem.   EdV V. .   EdV. .    E  0. qenc. 0. . Total charge. 1. 0.   dV. Charge density.