Electrostatics. Dielectric Polarization and Boundary Conditions
0 view 0 purchase
Course
B.S. Physics 2023
Institution
Mahatma Gandhi University Kottayam
This document gives a clear introduction to dielectric polarization and boundary conditions. This document is suitable for any graduate course in basic electrostatics. A concise and in-depth introduction to dielectric polarization is made. The application of electrostatic boundary conditions is d...
Electrostatics. dielectric polarization and boundary conditions
Subjects
electrostatics
polarization
polarizability
dielectric susceptibility
image charge
electrostatic boundary conditions
Written for
Mahatma Gandhi University Kottayam
B.S. Physics 2023
All documents for this subject (4)
Seller
Follow
blessonjs
Content preview
Introduction to Electrostatics. The Dielectric
Polarization and Dielectric Boundary conditions
1 Dielectric Polarization
Dielectrics are materials that lack free electrons; however, their behavior is altered when sub-
jected to an electric field. The electric field exerts a force on each charged molecule, causing
the positive charges to move in one direction and the negative charges to move in the opposite
direction. As a result, the centers of positive and negative charges shift from their average po-
sitions in opposing directions. This effect is referred to as polarization. To measure the impact
of an applied electric field on a dielectric, we introduce a vector known as polarization (P),
which is defined as the dipole moment per unit volume. The unit of polarization is C/m2 .
Taking all the elementary dipoles in a given volume, the polarization is
N
∑ Qj dqj
j=1
P = lim (1)
∆v→0 ∆v
P1 = Q1 d1 , P2 = Q2 d2 etc are small dipole moments in the volume considered.
1
, Consider a dielectric material with dipole moment P per unit volume.
The potential at point O, which is located outside the dielectric material, resulting from an
elemental dipole moment Pdv0 is
P.R̂dv0
dV = (2)
4πε0 R2
where R02 = (x − x0 )2 + (y − y0 )2 + (z − z0 )2 . R is the distance between the volume element dv0
at (x0 , y0 , z0 ) (source element) and O (x,y,z) (the field point). Now, we have
1
= [(x − x0 )2 + (y − y0 )2 + (z − z0 )2 ]−1/2 (3)
R
So,
(x − x0 )x̂ + (y − y0 )ŷ + (z − z0 )ẑ
1 R̂
∇ =− 0 2 0 2 0 2 3/2
=− 2 (4)
R [(x − x ) + (y − y ) + (z − z ) ] R
Similarly, the gradient with respect to the primed co-ordinates is
0 1 R̂
∇ = 2 (5)
R R
Therefore
P.R̂ 0 1
= P.∇ (6)
R2 R
2
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 blessonjs. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.29. You're not tied to anything after your purchase.
