The Electric Field

Electric and Magnetic Fields are Unified!

Working With the Electric Field

• Vector Field - watch the math!

• Coloumb’s Law:

• Electric Force:

30

1

4

qE r

r

electricF qE

Coulomb Force and Electric Field: Discrete to Continuous Cases• Imagine that you were

feeling really positive one fine day! If 0.01% of the protons in your body migrated to your head while the corresponding electrons went to your feet – estimate the size of the force acting on your body!

+ + + +

+ + + + + + + +

- - - - - - - - -- - -

Example...

4 m

3 m

E ?

-1 C+1 C

Find the electric field at E

X1 = (0,0) X2 = (4,0)

X = (4,-3)

1 21 23 3

1 21 2

x

y

E x x x xkQ kQE

E y y y yr r

VPython example

Electric Field: Discrete to Continuous Cases• For a finite charge distribution:

• Example: find the E field due to a water molecule at a point 1 nm from the O atom, along the axis of symmetry.

1

n

sum ii

E E

We have to make assumptions about q1 and q2: q1 = - 0.41e and q2 = 0.82 e

What do you expect the answer to be?

Discrete - Continuous Distributions• What happens as the number of charges

increases?

• Leads to new definition:

0

14 3

1 1

lim ( )limn n

ii i

n ni i i

dqE E r

r

0 0

1 14 43 2

ˆ( )V V

dq dqE r or r

r r

Example: Charged Ring

• Define an appropriate charge element “dq”

• We can set up the expression “formally” but may only be able to integrate under special symmetry conditions

• How do we handle “off-axis” calculations?

From Ring to Disk…

• Do the same calculation but this time for a uniformly charged disk.

• What happens if the radius of the disk becomes infinite?