Electrostatic force due to spherical shell of charge r R z

x y  

Spherical coordinates

x y     0 to  z

x y    0 to 2  r  0 to R z

x y   z

Electrostatic force due to spherical shell of charge r R z q0q0

R z r

R z r

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R z r  

R z r  

R z r   Only z-component survives

Electrostatic force due to spherical shell of charge R z r   Rcos  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 and  are NOT independent

Electrostatic force due to spherical shell of charge R z   r

R z r   r

R z   r

R z r  

Law of cosines

Electrostatic force due to spherical shell of charge R z r  

R z r

R z r

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R z r

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

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

Electrostatic force due to spherical shell of charge (inside the shell)