1. Electric Field Summary

2. The stinky field
If you have spent time around infants, you are likely familiar with the STINKY FIELD:
Stronger effect when you’re closer
Stronger effect with more concentrated source
Stronger effect on better detectors

3. Stinky field  Electric field
Stronger with more concentrated source
Only repulsive
Stronger closer to source
More pronounced effect on more sensitive detectors
Detected with test charges
Comes in discrete units
Detected with noses or gas chromatographs
Can be attractive

4. Electric Field
𝐸 ≝ 𝐹 𝑞
The strength of the electric field 𝐸 is defined as the force exerted on a miniscule test charge ( 𝑙𝑖𝑚 𝑞→0 ) .
The electric field strength describes the effect of the charges creating the electric field (and we ignore the electric field created by the test charge)
Reported in units of Newtons per Coulomb (N/C)

5. Quantifying Electric Field
𝐸 = 𝐹 𝑞 where 𝐹 =𝑘 𝑄𝑞 𝑟2 So, 𝐸 = 𝑘𝑄𝑞 𝑟2 𝑞 𝐸 =𝑘 𝑄 𝑟2
Strength of electric field is directly proportional to strength of source charge Q
Strength of electric field is inversely proportional to the square of the distance from the source charge

6. Example
A proton (q=1.6 x C) is released in a uniform electric field and experiences an electric force of 1.86 x N toward the south. What is the magnitude of the field? What is its direction? 𝑞=1.6 𝑥 10 −19 𝐶 𝐹 = 1.86 𝑥 10 −14 𝑁 𝐸 =?
𝐸 = 𝐹 𝑞 = 1.86 𝑥 10 −14 𝑁 1.6 𝑥 10 −19 𝐶
𝐸 =1.2 𝑥 𝑁 𝐶 south

7. Example
Determine the magnitude of acceleration experienced by an electron (q=-1.6 x C, m = 9.1 x kg) in an electric field of 756 N/C. 𝑞=−1.6 𝑥 10 −19 𝐶 𝑚=9.1 𝑥 10 −31 𝑘𝑔 𝐸 =756 𝑁 𝐶 𝑎=?
𝐸 = 𝐹 𝑞 where 𝐹 = 𝑚𝑎
So, 𝐸 = 𝑚𝑎 𝑞 so, 𝑎 =𝐸 𝑞 𝑚
𝑎 =(756 𝑁 𝐶 ) −1.6 𝑥 10 −19 𝐶 9.1 𝑥 10 −31 𝑘𝑔
𝑎 = 1.32 𝑥 𝑚 𝑠 /𝑠

8. Electric Potential

9. Difference in Electrical Potential Energy
In the case of a spring or an electric charge,
∆𝑈=−𝑊
where 𝑊= 𝐹𝑑
So, ∆𝑈 =−𝐹𝑑
where 𝐹=𝑞𝐸
So, ∆𝑈=−𝑞𝐸𝑑

10. Difference in Electrical Potential Energy
In the case of an electric charge,
∆𝑈=−𝑞𝐸𝑑
Change in potential depends on the distance between the two charges.
Change in potential depends on the strength of the electric field
Change in potential depends on size of test charge

11. Difference in Potential Energy / Charge
When describing forces induced by electric fields, it was useful to introduce 𝐸 as the strength of field in terms of force per charge, 𝐹 𝑞 . When dealing with differences in potential energy, it is useful to describe measure it in terms of energy difference per charge.

12. Difference in Potential Energy / Charge
We introduce a new term for difference in potential energy per charge: voltage, V
V≝ ∆𝑈 𝑞
Measured in Joules per Coulomb
Abbreviated as volts, V
Frequently referred to as ‘potential difference’
Named in honor of Alessandro Volta (1745 – 1827), inventor of first batteries

13. Quantifying voltage – part 1
V= ∆𝑈 𝑞 So, ∆𝑈=V𝑞
How much work can a given charge do?

14. Cliff  Potential difference
height = potential energy
mass = potential energy
∆𝑈 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝑚𝑔ℎ
voltage= potential energy
charge= potential energy
∆𝑈 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 =𝑞V

15. Typical voltages 108 V 105 V 1.5 to 9 V 10-4 V 120 V 106 V
Thundercloud to ground
108 V
High-voltage powerline
105 V
batteries
1.5 to 9 V
Potential changes on skin (EKG)
10-4 V
Household voltage (US)
120 V
Van der Graaf generator
106 V

16. Example
A electron (q=1.6 x C) is accelerated through a potential difference of V in old television. What is the change in electrical potential energy? 𝑞=−1.6 𝑥 10 −19 𝐶 V =5000 𝑉 ∆𝑈=?
∆𝑈=𝑞V=(−1.6 𝑥 10 −19 𝐶)(5000 𝐽 𝐶 )
∆𝑈=−8.0 𝑥 10 −16 𝐽
Potential energy is lost by electron (and converted into kinetic energy)

17. Quantifying voltage – part 2
∆𝑈=−𝑞𝐸𝑑
So, V=−𝐸𝑑
Or, 𝐸=− V 𝑑
Electric field strength is frequently reported in volts / meter

18. Example
An electric field of 525 V/m is desired between two parallel plates that are 11.0 mm apart. How large a voltage should be applied? 𝑑=11.0 𝑚𝑚 =1.1 𝑥 10 −2 𝑚 𝐸 =525 𝑉 𝑚 V=?
V=−𝐸𝑑=−(525 𝑉 𝑚 )(1.1 𝑥 10 −2 𝑚)
V=−5.8 𝑉
Note the convention: voltage, V
volts, V (italicized)

19. Implications
If you know the voltage difference and the distance between two plates, you can calculate the strength of the electric field…
And make capacitors
And electrocardiograms
And oscilloscopes
And televisions
And mass spectrometers
Etc.