Day18: Electric Dipole Potential & Determining E-Field from V

• The Electric Potential of an Electric Dipole

• Determination of the Electric Field from the Electric Potential

• The Gradient Operator

Electric Dipole Potential

• Two equal point charges Q, of

opposite sign, separated by a distance

l, is called an electric dipole

• The electric potential at an arbitrary

point P, due to an electric dipole is

The sum of the potentials due to each

charge

Electric Dipole Potential

• If we define p = Ql as dipole moment, then:

rrr

rQ

rrrQ

rr

Q

r

QV

0000 4

11

4

1

4

1

4

1

coscos, lrl

rlrfor

atordenotheinrneglectcanwerrif min,

20

200

cos

44)4 r

lQ

r

rQ

rrr

QV

20

cos

4

1

r

pV

Determination of the Electric Field from the Electric Potential

E

dl

A B• The potential difference between two points in

an electric field is known to be:

B

A

BA ldEVV

Determination of the Electric Field from the Electric Potential

• Re-write the electric potential in differential form and adding the x-, y- , and z – components of the electric field

• Define each electric field component as the partial derivatives of the electric potential in each direction

• Re-write as a vector equation.

Vz

ky

jx

iVVgradE

ˆˆˆ