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Electrostatic force due to spherical shell of charge. r. R. z. . y. . x. Spherical coordinates. z. 0 to . . y. . x. z. 0 to 0 to 2. r 0 to R. y. . x. . y. . x. z. Electrostatic force due to spherical shell of charge. r. R. q 0. z. - PowerPoint PPT Presentation
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Electrostatic force due to spherical shell of charge
rR
z
x
y
Spherical coordinates
x
y
0 to z
x
y
0 to
0 to 2
r 0 to R
z
x
y
z
Electrostatic force due to spherical shell of charge
r
R
z
24 R
q
ddRdAdq sin2
q0
2
20
20 sin
r
ddRkq
r
dqkqdF
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Fd
cosdF
Electrostatic force due to spherical shell of charge
R
z
r
Fd
cosdF
Electrostatic force due to spherical shell of charge
R
z
r
Fd
sindF
sindF
Only z-component survives
cosdFdFz
Electrostatic force due to spherical shell of charge
R
z
r
Rcos
r
Rz coscos
Why are we doing this?
To change variable to which is the polar angle
Electrostatic force due to spherical shell of charge
R
z
r
Rcos
r
Rz coscos
r
Rz
r
ddRkqdFdFz
cossincos
2
20
r
Rz
r
ddRkqdFz
cossin2
20
r and are NOT independent
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
r
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
Law of cosines
Electrostatic force due to spherical shell of charge
R
z
r
cos2222 RzzRr
zR
rzR
2cos
222
zR
rdrd
2
2sin
r
Rz
r
ddRkqdFz
cossin2
20
)cos(11
sin2
20 Rz
rd
rdRkqdFz
z
rzRz
rd
rzR
rdrRkqdFz 2
11 222
22
0
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2220
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2222
0
0'
2 r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
22222
0
0'
2
2
r
dr
z
rzRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
2
2222
0
0'
2 r
dr
z
rRzd
z
RkqdFz
Electrostatic force due to spherical shell of charge
R
z
r
drr
rRzd
z
RkqdFz
2
2222
020'
2
Electrostatic force due to spherical shell of charge
R
z
r
drr
Rzd
z
RkqdFz
1
2 2
222
020'
Electrostatic force due to spherical shell of charge
R
z
r
drr
Rz
z
RkqdFz
12
2 2
22
20'
Electrostatic force due to spherical shell of charge
R
z
r
Electrostatic force due to spherical shell of charge
R
z
r
r = z - R
Electrostatic force due to spherical shell of charge
R
z
r
r = z + R
Electrostatic force due to spherical shell of charge
drr
Rz
z
RkqF
Rz
Rz
z
1
2
22
20
Rz
Rz
z r
Rzr
z
RkqF
22
20
Rz
RzRz
Rz
RzRz
z
RkqFz
2222
20
RzRzRzRzz
RkqFz
20
RzRzRzRzz
RkqFz
20
RzRzRzRzz
RkqFz
20
Rz
RkqFz 4
20
2
20 4
z
RkqFz
20
z
qkqFz
Electrostatic force due to spherical shell of charge (inside the shell)
R
z
r
r = R - z
Electrostatic force due to spherical shell of charge (inside the shell)
R z
r
r = R + z
drr
Rz
z
RkqF
zR
zR
z
1
2
22
20
zR
zR
z r
Rzr
z
RkqF
22
20
zR
RzzR
zR
RzzR
z
RkqFz
2222
20
RzzRRzzRz
RkqFz
20
RzzRRzRzz
RkqFz
20
Electrostatic force due to spherical shell of charge (inside the shell)
0zF
Electrostatic force due to spherical shell of charge (inside the shell)
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