전자기학 4

소개글

전자기학 4에 대한 보고서 자료입니다.

목차

2.1 The Experimental Law of Coulomb

2.2 Electric Field Intensity

2.3 Field due to a continuous volume charge

2.4 Field of a line charge

2.5 Field of a sheet of charge

2.6 Streamlines and sketches of fields

본문내용

- When the charge is distributed over the volume,
Q_m
{vec r}_m
volume charge density at
{vec r}_m
:
rho_v ( {vec r}_m `)
or
rho_m ``rm{[C m^-3 ]}
small volume at
{vec r}_m
:
Delta v ( {vec r}_m `)
or
Delta v_m
Q_m ``=`` rho_m `` Delta v_m
Q ``=`` SUM from { {m}=1} to n Q_m ``=`` SUM from { {m}=1} to n rho_m `` Delta v_m
- When
Delta v ( {vec r}_m `)
or
Delta v_m
is infinitesimally small,
Q ``=`` Lim from { Delta v_m -> 0 } `` SUM from { {m}=1} to n rho_m `` Delta v_m ``=`` INT _v' ``{rho_v ( vec r' `)} `` dv'
(ex) calculate the charge inside a cylinder
Q ``=`` INT _v' ``{rho_v ( vec r' `)} `` dv'
INT _v' ``=`` INT _z=0.02^0.04 INT _phi=0^2pi INT _rho=0^0.01
rho_v ( vec r' `)} ``=`` -5 times 10^-6 `` e^{-10^5 rho z} ``rm{[C m^-3 ]}
dv' ``=`` d rho `` rho d phi `` dz
Q ``=`` - pi over 40 times 10^-12 ``rm{[C]}
(b) electric field intensity due to a continuous volume charge distribution
- electric field intensity due to multiple point charges,
Q_m
Q_m
vec E ( vec r `)
{vec r}_m
vec r
vec E ( vec r `) ``=`` SUM from { {m}=1} to n {Q_m} over {4 pi epsilon_o ` left| vec r `-` {vec r}_m `right|^2} {hat a}_m ``=`` SUM from { {m}=1} to n {Q_m} over {4 pi epsilon_o} {vec r `-` {vec r}_m} over {` left| vec r `-` {vec r}_m `right|^3}
- using a volume charge density
volume charge density at
{vec r}_m
:
rho_v ( {vec r}_m `)
or
rho_m
small volume at
{vec r}_m
:
Delta v ( {vec r}_m `)
or
Delta v_m
vec E ( vec r `) ``=`` SUM from { {m}=1} to n {Q_m} over {4 pi epsilon_o} {vec r `-` {vec r}_m} over {` left| vec r `-` {vec r}_m `right|^3} ``=`` SUM from { {m}=1} to n {rho_m `` Delta v_m} over {4 pi epsilon_o} {vec r `-` {vec r}_m} over {` left| vec r `-` {vec r}_m `right|^3}
- When
Delta v ( {vec r}_m `)
or
Delta v_m
is infinitesimally small,
Lim from { Delta v_m -> 0 } `` vec E ( vec r `) ``=`` Lim from { Delta v_m -> 0 } `` SUM from { {m}=1} to n {rho_m `` Delta v_m} over {4 pi epsilon_o} {vec r `-` {vec r}_m} over {` left| vec r `-` {vec r}_m `right|^3}
vec E ( vec r `) ``=`` INT _{v'} {rho_v ( vec r' `)} over {4 pi epsilon_o} {vec r `-` vec r'} over {` left| vec r `-` vec r' `right|^3} `` dv'
P. 37 D2.4
Problems. #6 #7 #11 #12

키워드

전자기학,   Experimental,   Coulomb,   continuous,   sketches,   Streamlines