Charge Conservation and Polarization

Charge Conservation Polarization Induced Dipole and Charges

PHYS 272 - David Blasing

Wednesday June 12th

1 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Quiz!!!!!!!!!

Name a main (red) result so far in the course. 1 point for the name of the result and 1 point for the formula/description.

2 / 23 So if one part of a system becomes positively charged, then another part of the system had to acquire an equal in magnitude amount of negative charge.

A ”neutral” object has a net charge of 0.

Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Charge is Conserved

Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change.

3 / 23 A ”neutral” object has a net charge of 0.

Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Charge is Conserved

Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change.

So if one part of a system becomes positively charged, then another part of the system had to acquire an equal in magnitude amount of negative charge.

3 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Charge is Conserved

Charge is Conserved The total (net sum) amount of charge in the system and its surroundings does not change.

So if one part of a system becomes positively charged, then another part of the system had to acquire an equal in magnitude amount of negative charge.

A ”neutral” object has a net charge of 0.

3 / 23 Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles

Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Examples of Neutral Atoms

Neutral atoms: number of electrons and protons is equal

Examples:

1 Hydrogen atom: 1 proton, 1 electron net charge ≡ Qtot = (+e) + (-e)=0

2 Sodium atom: 11 protons, 11 electrons =⇒ Qtot = 0

4 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Examples of Neutral Atoms

Neutral atoms: number of electrons and protons is equal

Examples:

1 Hydrogen atom: 1 proton, 1 electron net charge ≡ Qtot = (+e) + (-e)=0

2 Sodium atom: 11 protons, 11 electrons =⇒ Qtot = 0

Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles

4 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Objects can be charged in many ways

Note: the only charged objects that can be transferred by rubbing are positive or negative ions, or electrons Amount of energy required to remove bare nuclei or protons from inside the surface atoms is enormous

5 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Clicker Question 1

6 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Clicker Question 2

7 / 23 Charge Conservation Charge Conservation Polarization Charging Objects Induced Dipole and Charges Clicker Question 3

8 / 23 Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Hydrogen

Charge of electron cloud equals that of the nucleus so it’s a electrically neutral atom. If the electron cloud is centered on the nucleus then it produces no E~ ﬁeld 9 / 23 . Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization

Deﬁnition: Polarized Atom An atom is “polarized” when its electron cloud has been shifted by an external charge so that it is not centered on the nucleus.

Induced polarization (an induced dipole) is not permanent. Induced dipoles appear (disappear) by the presence (absence) of an E~ ﬁeld.

10 / 23 Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Hydrogen Polarizes in an E~ ﬁeld

Force due to the E~ ﬁeld created by positive charge pushes the electron cloud and nucleus in opposite directions, creating an electric dipole.

11 / 23 Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization Vector

Polarization Vector p~ = αE~

In most materials the polarization is proportional to the electric ﬁeld.

α is the “polarizability” of whatever particular material you are dealing with.

12 / 23 It was the combination q~s in dipoles. p~ = αE~ = q~s

Is the size an induced dipole constant?

No, it depends on the strength of the applied electric ﬁeld.

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Dimensional Analysis

Cm α has dimensions of N/C and that makes p~ have units of Cm.

You have actually seen p~ before, but we just didn’t call it polarization. Anyone have a guess where?

13 / 23 Is the size an induced dipole constant?

No, it depends on the strength of the applied electric ﬁeld.

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Dimensional Analysis

Cm α has dimensions of N/C and that makes p~ have units of Cm.

You have actually seen p~ before, but we just didn’t call it polarization. Anyone have a guess where?

It was the combination q~s in dipoles. p~ = αE~ = q~s

13 / 23 No, it depends on the strength of the applied electric ﬁeld.

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Dimensional Analysis

Cm α has dimensions of N/C and that makes p~ have units of Cm.

You have actually seen p~ before, but we just didn’t call it polarization. Anyone have a guess where?

It was the combination q~s in dipoles. p~ = αE~ = q~s

Is the size an induced dipole constant?

13 / 23 Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Dimensional Analysis

Cm α has dimensions of N/C and that makes p~ have units of Cm.

You have actually seen p~ before, but we just didn’t call it polarization. Anyone have a guess where?

It was the combination q~s in dipoles. p~ = αE~ = q~s

Is the size an induced dipole constant?

No, it depends on the strength of the applied electric ﬁeld.

13 / 23 A typical atomic polarizability is α = 10−40 Cm/(N/C).

|p~| = α|E~| = q|~s|

α =⇒ s = q E

If q = e (hydrogen) then plugging in numbers gives s = 2x10−15 m. This is about a factor of one hundred thousand smaller than the atom itself...very small shift for a pretty big electric ﬁeld. This is a small eﬀect.

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization Example

Question - If q=e (proton charge), what is the charge separation by applying a ﬁeld |E~| = 3 · 106N/C? (This is about the threshold to cause a spark).

14 / 23 |p~| = α|E~| = q|~s|

α =⇒ s = q E

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization Example

Question - If q=e (proton charge), what is the charge separation by applying a ﬁeld |E~| = 3 · 106N/C? (This is about the threshold to cause a spark).

A typical atomic polarizability is α = 10−40 Cm/(N/C).

14 / 23 If q = e (hydrogen) then plugging in numbers gives s = 2x10−15 m. This is about a factor of one hundred thousand smaller than the atom itself...very small shift for a pretty big electric ﬁeld. This is a small eﬀect.

Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization Example

Question - If q=e (proton charge), what is the charge separation by applying a ﬁeld |E~| = 3 · 106N/C? (This is about the threshold to cause a spark).

A typical atomic polarizability is α = 10−40 Cm/(N/C).

|p~| = α|E~| = q|~s|

α =⇒ s = q E

14 / 23 Charge Conservation Polarization Polarization Example Problem Induced Dipole and Charges Polarization Example

Question - If q=e (proton charge), what is the charge separation by applying a ﬁeld |E~| = 3 · 106N/C? (This is about the threshold to cause a spark).

A typical atomic polarizability is α = 10−40 Cm/(N/C).

|p~| = α|E~| = q|~s|

α =⇒ s = q E

14 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Clicker Question 4

Can a neutral object make an electric ﬁeld?

A. Yes B. No C. I don’t like physics.

15 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Neutral Objects

An electric dipole is a neutral object, but it does create a nonzero E~ ﬁeld around it.

Neutral objects can make nonzero electric ﬁelds in the space surrounding them. A uniformly neutral object will not make an electric ﬁeld though.

16 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Clicker Question 5

Does a neutral object experience a force from a point charge? A. Yes, attraction. B. Yes, repulsion C. No.

17 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Group Question

Why does a blown up ballon, after it is charged (maybe by rubbing it against your hair), stick to a wall?

18 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

19 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

20 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

21 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

22 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

22 / 23 So neutral objects are attracted by charges, but it is relatively 1 small. The force falls of like r 5 and α is typically very small.

Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

23 / 23 Charge Conservation Clicker Question Polarization Example Problem Induced Dipole and Charges Calculate the Force Between a Dipole and a Point Charge

So neutral objects are attracted by charges, but it is relatively 1 small. The force falls of like r 5 and α is typically very small. 23 / 23