Electrostatics

The Electric Charge

Electrostatics

Background

...

 Electrostatics

      Electric Charge

           Textbook Section 5.1

 Electrostatics

      Electric Charge

           ... is fundamental

Once upon a time ...

 Electrostatics

      Electric Charge

           ... is fundamental -- the phenomenological approach

Mr P explaining electric charge in terms of what it does.

 Electrostatics

      Electric Charge

           ... is fundamental

Once upon a time ...

in the 20th century ...

Experimental basis of QM

    Discovery of the X Ray and the Electron

          Thomson's experiment -- electron charge to mass ratio (1897)

From T & R, p 86

J.J. Thomson showed that cathode-rays were charged particles by showing their deflection in magnetic/electric fields.

Furthermore, he managed to measure the charge to mass ratio of the electron.

Experimental basis of QM

    Discovery of the X Ray and the Electron

          Thomson's experiment -- electron charge to mass ratio (1897)

From T & R, p 86

Experimental basis of QM

    Determination of the electron charge

          Millikan's experiment -- electron charge (1911)

From T & R, p 89

Millikan suspended oil drops between two plates by changing the potential difference across the plates.

The equilibrium between the force of gravity and the electric force gave an estimate of the charge on the oil drop, in terms of its volume.

The volume was estimated from the terminal velocity.

Millikan found that the drops carried electric charge that was quantized!

The elementary charge, he found, was

e=1.602\times10^{-19}C

more on wikipedia

Experimental basis of QM

    Determination of the electron charge

          Millikan's experiment -- electron charge (1911)

The atomic nucleus

What lies within?

The variety of nuclei

Atomic Nucleus

      Nucleons & their structure

           Rutherford

Atomic Nucleus

      Nucleons & their structure

           Discovery of the neutron (1932)

Chadwick suggested the radiation was a neutral particle

of about the same mass as a proton.

Atomic Nucleus

           Chart of the nuclides

      The variety of nuclei

Atomic Nucleus

           Chart of the nuclides

      The variety of nuclei

Atomic Nucleus

           Chart of the nuclides

      The variety of nuclei

Atomic Nucleus

      The variety of nuclei

           Definitions

Isotope:

Atoms with same Z but different A

Nuclide:

A nuclear species with a given Z, N, and A

Isotone:

Atoms with same N but different A

Isobar:

Atoms with same A but different combination of Z and N

Atomic Nucleus

           Size of the nucleus 

Atomic nuclei are bound states of protons + neutrons

Probability density for the presence of neutrons and protons predicted for the neon-20 nucleus. It can be seen that this is not homogeneous: the neutrons and protons are distributed in clusters. © Jean-Paul Ebran/CEA

      Nucleons & their structure

The spatial extension of a typical nucleus is ~ fm

The comparative spatial extension of the atomic nucleus to the spatial extension of the electronic cloud in an atom is of the same order as the ratio of the size of your thumb compared to the size of UCF campus.

Atomic Nucleus

           Underlying structure

Atomic nuclei are bound states of protons + neutrons

Probability density for the presence of neutrons and protons predicted for the neon-20 nucleus. It can be seen that this is not homogeneous: the neutrons and protons are distributed in clusters. © Jean-Paul Ebran/CEA

protons & neutrons

have internal structure

      Nucleons & their structure

proton

neutron

Atomic Nucleus

           Underlying structure

The Standard Model

of Elementary Particles

      Nucleons & their structure

Electrostatics

The Electric Charge

... is fundamental

 Electrostatics

      Electric Charge

           TL;DR

  • Electric Charge is an intrinsic property of matter.
e=1.602\times10^{-19}C
  • Electric Charge is quantized (i.e. manifests in nature in integer multiples of the elementary charge:
  • We have identified two types of charge -- ka positive and negative.
  • "Ordinary" matter is made up of atoms, who are themselves made up of protons, neutrons, and electrons. 
  • Neutral objects have equal number of protons and electrons. (neutral does not mean without charge.)

 Electrostatics

      Electric Charge

           The Net Electric Charge

  • Each Proton has a net charge of +e
  • Each Electron has a net charge of -e
  • Objects are charged by losing or gaining electrons.
  • Every ordinary object will carry a net charge that depends on the difference between the number of protons and electrons:
q_\text{net}=n_p \times q_p + n_e \times q_e
=n_p \times e + n_e \times (-e)
=(n_p - n_e) \times e
  • Thus, an object will carry net negative charge if it has an excess of electrons, while a deficiency of electrons results in an overall positive net charge. 

Electrostatics

The Electric Charge

How to "charge" an object

 Electrostatics

      Electric Charge

           Charging by contact

  • Electric Charge is conserved in a closed system.
  • When two objects are in "contact", they could exchange electrons, leaving one object positively charged and the other negatively charged.

Move John's feet against the carpet and see the charges jump from the carpet to his body.

 Electrostatics

      Electric Charge

           Conductors & Insulators

In conductors, some electrons are free to move

In insulators, electrons are bound to the nuclei

 Electrostatics

      Electric Charge

           Conservation of charge

 Electrostatics

      Electric Charge

           Polarization

  • You can induce a charge on an object by performing a series of steps, that typically start with polarization.
  • Polarization means separating the charges to different "poles"
  • Polarization means separating the charges to different "poles"
  • Rub the balloon against the sweater to pick up some charge.
  • Notice the charge sits in place on the balloon -- why? (hint: is it made out of a conducting or insulating material?)
  • Bring the balloon close to the wall -- the charges in the wall polarize.

 Electrostatics

      Electric Charge

           Charing by induction

Electrostatics

The Electric Charge

Charge Distribution

 Electrostatics

      Electric Charge

           Charge Distributions

\lambda = dq / dl

Linear Charge Density

\sigma=dq / dA

Surface Charge Density

\rho=dq / dV

Volume Charge Density

\lambda_\text{\tiny uniform} = \frac{Q_\text{\tiny total}}{l_\text{\tiny total}}
\sigma\text{\tiny uniform} = \frac{Q_\text{\tiny total}}{A_\text{\tiny total}}
\rho\text{\tiny uniform} = \frac{Q_\text{\tiny total}}{V_\text{\tiny total}}

 Electrostatics

      Electric Charge

           Point Charge

Charge distribution A

Charge distribution B

What do we mean by point charges?

\text{size$_\text{charge distribution}$}
\text{scale of analysis}
\lt\lt\lt

 Electrostatics

      Electric Charge

           Di-pole

What is an electric dipole?

Two equal but opposite charges separated by a small distance. 

The electric dipole moment 

The electric dipole moment p is a vector whose direction is from -q to +q and whose magnitude is given by p=qd

Electrostatics

The Electric Charge

... and the rest of the cast

 Electrostatics

      The influence & interaction of electric charges

           The Cast 

q
\vec{E}
V
\Phi
\vec{F}
U

potential

potential energy

field

force

charge

flux

influence

interaction

Electric ....

 Electrostatics

      The influence & interaction of electric charges

           The Cast - relationship map

Electric ....

\vec{E}
V
\Phi

influence

interaction

\ \vec{E}=-\vec{\nabla} V\
\ \Delta V = \int \vec{E}\cdot d\vec{s}\
\ \Phi = \int \vec{E}\cdot d\vec{A}\
\vec{F}
U
\ \vec{F}=-\vec{\nabla} U\
\ \Delta U = \int \vec{F}\cdot d\vec{s}\
\ \vec{F} = q_0\ \vec{E}\
\ \vec{E} = \vec{F}/q_0\ \
\ U = q_0\ V\
\ V = U/q_0\ \
q

 Electrostatics

      The influence & interaction of electric charges

           The Cast - relationship map

Electric ....

\vec{E}
V
\Phi

influence

interaction

\ \vec{E}=-\vec{\nabla} V\
\ \Delta V = \int \vec{E}\cdot d\vec{s}\
\ \Phi = \int \vec{E}\cdot d\vec{A}\
\vec{F}
U
\ \vec{F}=-\vec{\nabla} U\
\ \Delta U = \int \vec{F}\cdot d\vec{s}\
\ \vec{F} = q_0\ \vec{E}\
\ \vec{E} = \vec{F}/q_0\ \
\ U = q_0\ V\quad
\ V = U/q_0\ \
q
\Phi_g

influence

\ \Phi_g = \int \vec{g}\cdot d\vec{A}\
\vec{g}
gy
\ \vec{g}=-\vec{\nabla} (gy)\
\ \Delta V = \int \vec{g}\cdot d\vec{s}\
\vec{F}_g
mgy

interaction

\ \vec{F}=-\vec{\nabla} (mgy)\\ =-mg\hat j
\ \Delta U = -\int \vec{F}\cdot d\vec{s}\
m
\ \vec{F_g} = m\ \vec{g}\
\ \vec{g} = \vec{F_g}/m\ \
\ U_g = m\ V_g\
\ V_g = U_g/m\ \

gravitational....

analogus to

 Electrostatics

      The influence & interaction of electric charges

           The Cast 

q
\vec{F}
U
\Phi

influence

interaction

Physical Quantities

\ \vec{E}=-\vec{\nabla} V\
\ \Delta V = -\int \vec{E}\cdot d\vec{s}\
\ \Phi = \int \vec{E}\cdot d\vec{A}\
\vec{E}
V
\ \vec{F}=-\vec{\nabla} U\
\ \Delta U = -\int \vec{F}\cdot d\vec{s}\
\ \vec{F} = q_0\ \vec{E}\
\ \vec{E} = \vec{F}/q_0\ \
\ U = q_0\ V\
\ V = U/q_0\ \

 Electrostatics

      The influence & interaction of electric charges

           The Cast 

electric charge

q
\vec{F}
\vec{E}
U
V
\Phi

electric charge influences

interaction between charges

Physical Quantities

 Electrostatics

      The influence & interaction of electric charges

           The Cast 

recurring roles

\vec{r}
\hat{r}
\hat{n}
\hat{r}=\frac{\vec{r}}{r} \text{ is a unit vector in direction of $\vec{r}$}
\text{ Relative Position Vector}

 Electrostatics

      The influence & interaction of electric charges

           The Cast 

charge

q
\vec{F}
\vec{E}
U
V
\Phi

influence

interaction

Physical Quantities

recurring roles

Parameters

\vec{r}
\hat{r}
\hat{n}
\hat{r}=\frac{\vec{r}}{r} \text{ is a unit vector in direction of $\vec{r}$}