Electric Potential and Electric Field: Concepts, Formulas, and Applications, Study notes of Basic Electronics

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Electric Potential

• Electric Potential energy:
• Electric Potential:

b  U (^) elec  a F^ elec^  dl 

b  V  a E dl

Field is the (negative of) the Gradient

of Potential

x y z

F dU dx U F dU dy F dU dz

        

F

x y z

E dV dx V E dV dy E dV dz

        

E

Electric field of single point charge

E =^ kqr 2 r ˆ 

Electric potential of single point charge

2 2

b a b a

V

kqr V kqr

E dl E r r dl

Electric potential of single point charge

2 2

0 by convention

b a b a b a b a

V

kqr V kqr V V V kqr kqr V kqr const

E dl E r r dl

Potential for Multiple Charges

E  E 1  E 2  E 3 

b a b b b a a a

 V  

E dl

E dl E dl E dl

V  V 1  V 2  V 3  

Finding the Electric Field due to

Continuous Charge Distributions

• When possible, use symmetry to eliminate one or more component of the electric field.
• Define a (linear, areal or volume) density torelate small spatial regions to small bits of charge.
• Calculate the electric field due to each small charge bit:.
• Sum up (integrate) the electric fields to find the total field.

dE  k rdq 2

Finding the Potential due to Continuous

Charge Distributions

• When possible, use symmetry to eliminate one or more component of the electric field.
• Define a (linear, areal or volume) density torelate small spatial regions to small bits of charge.
• Calculate the potential due to each small charge bit:.
• Sum up (integrate) the potentials to find the total potential.

dV k dqr

Spherical shell of charge

 

2 ˆ 0

a constant

out in out in

kQr (^) r R r R V kQr r R V kQR r R

       

E r E

 