the electric field electric and magnetic fields are unified!
TRANSCRIPT
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The Electric Field
Electric and Magnetic Fields are Unified!
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Working With the Electric Field
• Vector Field - watch the math!
• Coloumb’s Law:
• Electric Force:
30
1
4
qE r
r
electricF qE
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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!
+ + + +
+ + + + + + + +
- - - - - - - - -- - -
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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
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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
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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?
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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
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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?
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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?