8/17/2019 tsl94.pdf

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Electric Potential of a Uniformly Charged Solid Sphere

•  Electric charge on sphere:  Q  = ρV    =  4π

3  ρR

3

•   Electric field at r > R:  E  =  kQ

r2

•   Electric field at r < R:  E  =  kQ

R3  r

•  Electric potential at  r > R:

V    = −Z   r∞

kQr2

  dr  =   kQr

•  Electric potential at  r < R:

V    = −Z   R∞

kQr2

  dr −Z   rR

kQR3

  r dr

⇒ V    =  kQ

R

  −kQ

2R

3 `r2− R

2

´  =  kQ

2R„3−

r2

R

2«

tsl94 – p.1/1