Full summary of "Fysica : Elektromagnetisme" which is a course seen in 2nd year bachelor of chemistry in Vrije Universiteit Brussel
It is a resume that was made from the textbook Physics for Scientists and Engineers from Randall D. Knight
Part vi electricity and magnetism (chapter 22 --> chapter 32)
January 29, 2022
86
2021/2022
Summary
Subjects
physics
electricity
magnetism
elektromagnetisme
electromagnetic
fysica
d knight
Connected book
Book Title:
Author(s):
Edition:
ISBN:
Edition:
Written for
Vrije Universiteit Brussel (VUB)
Chemie
Fysica : Elektromagnetisme
All documents for this subject (2)
Seller
Follow
simongabay
Content preview
Chapter 22 : Electric charges and forces
Coulomb’s Law
The forces between 2 charged particles 𝒒𝟏 and 𝒒𝟐 separated by distance 𝒓 are :
𝐾|𝑞1 ||𝑞2 |
𝐹1 𝑜𝑛 2 = 𝐹2 𝑜𝑛 1 =
𝑟2
1
Where 𝐾 = is called the electrostatic constant
4𝜋𝜀0
- Coulomb’s law applies only to point charges
- Electric forces, like other forces, can be superimposed
- The forces are repulsive for 2 like charges, attractive for 2 opposite charges
The Charge Model
There are two kinds of charge, positive and negative :
- Fundamental charges are protons and electrons, with charge ±𝑒 with 𝑒 being the
fundamental unit of charge (𝑒 = 1.60 ∙ 10−19 𝐶)
- Objects are charged by adding or removing electrons
→ Charge varies by discrete steps , not continuously (=charge quantization)
- The amount of charge is 𝑞 = (𝑁𝑝 − 𝑁𝑒 )𝑒
- A neutral object has no charge
- Charge is neither created nor destroyed (=law of conservation of charge)
There are two types of material, insulators and conductors :
- Charge remains fixed in or on an insulator
- Charge moves easily through or along conductors
- Charge is transferred by contact between objects
NOTE Both insulators and conductors can be charged, they differ in the mobility of the charge
Charged objects attract neutral objects :
- Charge polarizes metal by shifting the electron sea
- Charge polarizes atoms, creating electric dipoles
- The polarization force is always an attractive force
,The Electroscope
The process by which an electroscope is charged :
The Field Model
Charges interact with each other via the electric field 𝐸⃗ :
- Charges alter the space around themselves by creating an electric field
- The field is the agent that exerts a force
An electric field is identified and measured in terms of the force on a positive probe charge 𝑞 :
𝐹𝑜𝑛 𝑞
𝐸⃗ =
𝑞
- The electric field exists at all points in space
- An electric field vector shows the field only at one point, the point at the tail of the vector
,Chapter 23 : The Electric Field
Point Charge (with charge 𝑞)
The force that a point charge 𝑞 exerts on a probe charge 𝑞′ is equal to
1 𝑞𝑞′
𝐹⃗𝑜𝑛 𝑞′ = ( , 𝑎𝑤𝑎𝑦 𝑓𝑟𝑜𝑚 𝑞)
4𝜋𝜀0 𝑟 2
The electric field of the source charge 𝑞 is then equal to
𝐹⃗𝑜𝑛 𝑞′ 1 𝑞
𝐸⃗⃗ = = 𝑟̂
𝑞′ 4𝜋𝜀0 𝑟 2
𝐶2
With 𝑟̂ being a vector unit pointing away from source charge 𝑞 and 𝜀0 = 8,55 ∙ 10−12 𝑁𝑚2
Multiple charges
Electric fields obey the principle of superposition
Limiting cases
(𝐸𝑛𝑒𝑡 )𝑧 = 0 → in the 𝑥𝑦-plane
(𝐸𝑛𝑒𝑡 )𝑦 = 0 → 𝐸1 and 𝐸3 have equal magnitudes and tilted with same angle 𝜃
(𝐸𝑛𝑒𝑡 )𝑥 = (𝐸1 )𝑥 + (𝐸2 )𝑥 + (𝐸3 )𝑥 = 2(𝐸1 )𝑥 + (𝐸2 )𝑥
1 𝑞2 1 𝑞
(𝐸2 )𝑥 = 𝐸2 = 2 = (𝑟2 = 𝑥)
4𝜋𝜀0 𝑟2 4𝜋𝜀0 𝑥 2
1 𝑞1
(𝐸1 )𝑥 = 𝐸1 cos 𝜃 = cos 𝜃
4𝜋𝜀0 𝑟12
𝑟1 and 𝜃 both vary with position 𝑥 𝑥
𝑥, they need to be expressed in Pythagorean Theorem : 𝑟1 = √𝑥 2 + 𝑑 2 cos 𝜃 = =
𝑟1 √𝑥 2 + 𝑑 2
function of 𝑥
1 𝑞 𝑥 1 𝑥𝑞
(𝐸1 )𝑥 = =
4𝜋𝜀0 𝑥 + 𝑑 √𝑥 2 + 𝑑2 4𝜋𝜀0 (𝑥 2 + 𝑑2 )32
2 2
, 2 cases :
- 𝑥 ≪ 𝑑 (𝑥 → 0)
Becomes a single point charge 𝑞 at the origin (𝐸⃗⃗1 and 𝐸⃗⃗3 become opposite and cancel)
2𝑥
lim 3 =0 (approximating 0)
𝑥→0 (𝑥 2 +𝑑2 )2
1 𝑞
→ 𝐸𝑛𝑒𝑡 = 4𝜋𝜀 𝑥2
= Field of single point charge
0
1
In no 𝑑, thus no approximation
𝑥2
- 𝑥 ≫ 𝑑 (𝑥 → ∞)
The field is zero in the limit 𝑥 → ∞. Doesn’t tell much, 𝑥 just has to be very large in
comparison to the spacing 𝑑 between the source charges.
Then the denominator of the second term is well approximated by :
3 3
(𝑥 2 + 𝑑2 )2 ≈ (𝑥 2 )2 = 𝑥 3
1 2𝑥 1 2𝑥 3
Thus, lim (𝑥 2 + 3 ) = 𝑥2 + 𝑥3 = 𝑥2
𝑥≫𝑑 (𝑥 2 +𝑑 2 )2
1 3𝑞
𝐸⃗⃗𝑛𝑒𝑡 = 4𝜋𝜀 î this is the electric field op a point charge 3𝑞
0 𝑥2
Dipole
Two equal but opposite charges ±𝑞 separated by a small distance 𝑠 form an electric dipole :
- Permanent electric dipole (ex. water molecule)
- Induced electric dipole (polarizing a neutral atom with an external electric field)
In practice, electric field of a dipole always observed at distances 𝑦 ≫ 𝑠, distances much larger
than the charge separation.
1 2 1 2
Denominator can be approximated (𝑦 − 2 𝑠) (𝑦 + 2 𝑠) ≈ 𝑦 4
1 2𝑞𝑠
(𝐸𝑑𝑖𝑝𝑜𝑙𝑒 )𝑦 ≈
4𝜋𝜀0 𝑦 3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller simongabay. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.90. You're not tied to anything after your purchase.
