5.7 Electric dipoles (Page 2/6)

University physics volume 2 Page 2 / 6

A dipole, consisting of a negative charge on the left and a positive charge on the right is in a uniform electric field pointing to the right. The dipole moment, p, points to the right. The field lines of the net electric field are the sum of the dipole field and the uniform external field, horizontal far from the dipole and similar to the dipole field near the dipole. — The net electric field is the vector sum of the field of the dipole plus the external field.

Recall that we found the electric field of a dipole in [link] . If we rewrite it in terms of the dipole moment we get:

\vec{E} (z) = \frac{1}{4 π ε_{0}} \frac{\vec{p}}{z^{3}} .

The form of this field is shown in [link] . Notice that along the plane perpendicular to the axis of the dipole and midway between the charges, the direction of the electric field is opposite that of the dipole and gets weaker the further from the axis one goes. Similarly, on the axis of the dipole (but outside it), the field points in the same direction as the dipole, again getting weaker the further one gets from the charges.

Summary

If a permanent dipole is placed in an external electric field, it results in a torque that aligns it with the external field.
If a nonpolar atom (or molecule) is placed in an external field, it gains an induced dipole that is aligned with the external field.
The net field is the vector sum of the external field plus the field of the dipole (physical or induced).
The strength of the polarization is described by the dipole moment of the dipole, $\vec{p} = q \vec{d}$ .

Key equations

Coulomb’s law	${\vec{F}}_{12} (r) = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r_{12}^{2}} {\hat{r}}_{12}$
Superposition of electric forces	$\vec{F} (r) = \frac{1}{4 π ε_{0}} Q \sum_{i = 1}^{N} \frac{q_{i}}{r_{i}^{2}} {\hat{r}}_{i}$
Electric force due to an electric field	$\vec{F} = Q \vec{E}$
Electric field at point P	$\vec{E} (P) \equiv \frac{1}{4 π ε_{0}} \sum_{i = 1}^{N} \frac{q_{i}}{r_{i}^{2}} {\hat{r}}_{i}$
Field of an infinite wire	$\vec{E} (z) = \frac{1}{4 π ε_{0}} \frac{2 λ}{z} \hat{k}$
Field of an infinite plane	$\vec{E} = \frac{σ}{2 ε_{0}} \hat{k}$
Dipole moment	$\vec{p} \equiv q \vec{d}$
Torque on dipole in external E-field	$\vec{τ} = \vec{p} \times \vec{E}$

Conceptual questions

What are the stable orientation(s) for a dipole in an external electric field? What happens if the dipole is slightly perturbed from these orientations?

Got questions? Get instant answers now!

Problems

Consider the equal and opposite charges shown below. (a) Show that at all points on the x -axis for which $| x | ≫ a, E \approx {Q a / 2 π ε}_{0} x^{3} .$ (b) Show that at all points on the y -axis for which $| y | ≫ a, E \approx {Q a / π ε}_{0} y^{3} .$

Two charges are shown on the y axis of an x y coordinate system. Charge +Q is a distance a above the origin, and charge −Q is a distance a below the origin.

$E_{x} = 0,$
$E_{y} = \frac{1}{4 π ε_{0}} [\frac{2 q}{(x^{2} + a^{2})} \frac{a}{\sqrt{(x^{2} + a^{2})}}]$
$\Rightarrow x ≫ a \Rightarrow \frac{1}{2 π ε_{0}} \frac{q a}{x^{3}}$ ,
$E_{y} = \frac{q}{4 π ε_{0}} [\frac{2 y a + 2 y a}{{(y - a)}^{2} {(y + a)}^{2}}]$
$\Rightarrow y ≫ a \Rightarrow \frac{1}{π ε_{0}} \frac{q a}{y^{3}}$

Got questions? Get instant answers now!

(a) What is the dipole moment of the configuration shown above? If $Q = 4.0 μ C$ , (b) what is the torque on this dipole with an electric field of $4.0 \times 10^{5} N/C \hat{i}$ ? (c) What is the torque on this dipole with an electric field of $−4.0 \times 10^{5} N/C \hat{i}$ ? (d) What is the torque on this dipole with an electric field of $\pm 4.0 \times 10^{5} N/C \hat{j}$ ?

Got questions? Get instant answers now!

A water molecule consists of two hydrogen atoms bonded with one oxygen atom. The bond angle between the two hydrogen atoms is $104 °$ (see below). Calculate the net dipole moment of a water molecule that is placed in a uniform, horizontal electric field of magnitude $2.3 \times 10^{−8} N/C .$ (You are missing some information for solving this problem; you will need to determine what information you need, and look it up.)

A schematic representation of the outer electron cloud of a neutral water molecule is shown. Three atoms are at the vertices of a triangle. The hydrogen atom has positive q charge and the oxygen atom has minus two q charge, and the angle between the line joining each hydrogen atom with the oxygen atom is one hundred and four degrees. The cloud density is shown as being greater at the oxygen atom.

The net dipole moment of the molecule is the vector sum of the individual dipole moments between the two O-H. The separation O-H is 0.9578 angstroms:
$\vec{p} = 1.889 \times 10^{−29} Cm \hat{i}$

Got questions? Get instant answers now!

Additional problems

Point charges $q_{1} = 2.0 μ C$ and $q_{1} = 4.0 μ C$ are located at $r_{1} = (4.0 \hat{i} - 2.0 \hat{j} + 2.0 \hat{k}) m$ and $r_{2} = (8.0 \hat{i} + 5.0 \hat{j} - 9.0 \hat{k}) m$ . What is the force of $q_{2} on q_{1} ?$

Got questions? Get instant answers now!

What is the force on the $5.0 - μ C$ charges shown below?

The following charges are shown on an x y coordinate system: Minus 3.0 micro Coulomb on the x axis, 3.0 meters to the left of the origin. Positive 5.0 micro Coulomb at the origin. Positive 9.0 micro Coulomb on the x axis, 3.0 meters to the right of the origin. Positive 6.0 micro Coulomb on the y axis, 3.0 meters above the origin.

${\vec{F}}_{net} = [−8.99 \times 10^{9} \frac{3.0 \times 10^{−6} (5.0 \times 10^{−6})}{{(3.0 m)}^{2}} - 8.99 \times 10^{9} \frac{9.0 \times 10^{−6} (5.0 \times 10^{−6})}{{(3.0 m)}^{2}}] \hat{i}$ ,
$−8.99 \times 10^{9} \frac{6.0 \times 10^{−6} (5.0 \times 10^{−6})}{{(3.0 m)}^{2}} \hat{j} = −0.06 N \hat{i} - 0.03 N \hat{j}$

Got questions? Get instant answers now!

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.

Kate Reply

To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.

Muhammed

What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?

Kate Reply

what is the change in momentum of a body?

Eunice Reply

what is a capacitor?

Raymond Reply

Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.

Gautam

A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate

Maria Reply

please solve

Sharon

8m/s²

Aishat

What is Thermodynamics

Muordit

velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.

Mehmet

A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat

Saheed Reply

50 m/s due south east

Someone

which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer

Ramon Reply

I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.

Someone

Scratch that

Someone

temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....

Someone

about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle

Someone

definitely of physics

Haryormhidey Reply

how many start and codon

Esrael Reply

what is field

Felix Reply

physics, biology and chemistry this is my Field

ALIYU

field is a region of space under the influence of some physical properties

Collete

what is ogarnic chemistry

WISDOM Reply

determine the slope giving that 3y+ 2x-14=0

WISDOM

Another formula for Acceleration

Belty Reply

a=v/t. a=f/m a

IHUMA

innocent

Adah

pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?

Nassze Reply

how do lnternal energy measures

Esrael

Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

JALLAH Reply

No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.

Dlovan

Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?

Robert

like charges repel while unlike charges atttact

Raymond

What is specific heat capacity

Destiny Reply

Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).

AI-Robot

specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin

ROKEEB

<< Chapter < Page Page > Chapter >>

Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask

	NCE Ch 08 Appraisal By Anh Dao Start Quiz
©flickr: BK	Self Confidence By Miranda Reising Start Quiz
	4 Psychology MCQ 2009 Final Exam By John Gabrieli Start Exam
	1 Neuroanatomy 01 The Cranial Nerves By Stephen Voron Start Quiz
	11 AP 11 Muscular System MCQ By OpenStax Start Quiz
	4 Neuroanatomy 04 Spinal Cord Brain Stem By Stephen Voron Start Quiz
	16 Biology 16 Gene Expression MCQ By OpenStax Start Quiz
	22 Biology 22 Prokaryotes Bacteria and Archaea MCQ By OpenStax Start Quiz
	Microeconomics Practice MCQ By Frank Levy Start Test
	2 AP 02 Chemical Level of Organization Essay By OpenStax Start Flashcards