The Electric The Electric Field I: discrete Field I: discrete

chargechargeChapter 21Chapter 21

©2008 by W.H. Freeman and Company

ChargesCharges

Similar charges repelSimilar charges repel Opposite charge attractOpposite charge attract

Charge is quantized and Charge is quantized and conservedconserved

Charge comes in little packetsCharge comes in little packets

The amount of charge is always The amount of charge is always conservedconserved

21-21

A plastic rod is rubbed against a wool shirt, thereby acquiring a charge of -0.80 μC. How many electrons are transferred from the wool shirt to the plastic rod?

Electric charges of the Electric charges of the opposite sign opposite sign

A.A. attract each other. attract each other.

B.B. exert no forces on each other. exert no forces on each other.

C.C.repel each other.repel each other.

Experimental evidence Experimental evidence indicates that indicates that

A.A. charge is quantized and conserved. charge is quantized and conserved.

B.B. charge is quantized but not charge is quantized but not conserved. conserved.

C.C. charge is conserved but not charge is conserved but not quantized. quantized.

D.D.charge is neither quantized nor charge is neither quantized nor conserved. conserved.

How many electrons must be How many electrons must be transferred to a body to produce a transferred to a body to produce a

charge of 125 nC? charge of 125 nC?

A.A. 1.25 1.25 10 10–7 –7

B.B. 1.60 1.60 10 10–19 –19

C.C.1.28 1.28 10 1012 12

D.D.3.45 3.45 10 101111

E.E. 7.81 7.81 10 101111

Three kinds of materialsThree kinds of materials

ConductorsConductorsmaterials through which charge can materials through which charge can

move rather freelymove rather freely InsulatorsInsulators

materials through which charge materials through which charge cannot move freely cannot move freely

Note: These are RELATIVE categoriesNote: These are RELATIVE categories

Charging by inductionCharging by induction

Coulomb’s lawCoulomb’s law

Force due to charge is related to the Force due to charge is related to the amounts of charge and the distance amounts of charge and the distance between them squaredbetween them squared

FF in Newtons in Newtons qq in coulombs in coulombs rr in meters in meters kk is ??? is ???

UnitsUnits

Units of Units of kk are empirical are empirical More “realistic” units areMore “realistic” units are

21-2621-26

A point charge A point charge qq11 = 4.0 = 4.0 μμC is at the C is at the origin and a point charge origin and a point charge qq22 = 6.0 = 6.0 μμC is on the C is on the xx axis at axis at xx = 3.0 m. ( = 3.0 m. (aa) ) Find the electric force on charge Find the electric force on charge qq22. . ((bb) Find the electric force on ) Find the electric force on qq11. (. (cc) ) How would your answers for Parts How would your answers for Parts ((aa) and () and (bb) differ if ) differ if qq22 were -6.0 were -6.0 μμC?C?

Superposition Superposition Electrostatic forces – like all forces - obey Electrostatic forces – like all forces - obey

superpositionsuperposition

Add vectorially – use componentsAdd vectorially – use components

21-3621-36

The structure of the The structure of the NHNH33 molecule is molecule is approximately that of an equilateral approximately that of an equilateral tetrahedron, with three Htetrahedron, with three H++ ions ions forming the base and an Nforming the base and an N3-3- ion at ion at the apex of the tetrahedron. The the apex of the tetrahedron. The length of each side is 1.64 × 10length of each side is 1.64 × 10-10-10 m. m. Calculate the electric force that acts Calculate the electric force that acts on each ion.on each ion.

21-36

The Electric Field

We can define the electric field at some point near the charged object, such as point P: We first place a positive charge q0, a test charge, at the point. We then measure the electrostatic force F that acts on the test charge. Finally, we define the electric field E at point P due to the charged object as Fig. 21-11

Units

What are the units of the electric field?

Newton per Coulomb

When a 2.0-nC point charge is placed at the origin, it experiences an electric force of 8.0 × 10-4 N in the +y direction. (a) What is the electric field at the origin? (b) What would be the electric force on a -4.0-nC point charge placed at the origin? (c) If this force is due to the electric field of a point charge on the y axis at y = 3.0 cm, what is the value of that charge?

39 •

21.5 Electric field lines – a single point charge

Lines originate on positive charges; terminate on negative charges

Number of lines proportional to size of charge

Density of lines proportional to magnitude of electric field

41 •• Two point charges q1 and q2 both have a charge equal to +6.0 nC and are on the y axis at y1 = +3.0 cm and y2 = -3.0 cm, respectively. (a) What are the magnitude and direction of the electric field on the x axis at x = 4.0 cm? (b) What is the force exerted on a third charge q0 = 2.0 nC when it is placed on the x axis at x = 4.0 cm?

If you bring a positively charged insulator near two uncharged metallic spheres that are in contact and then separate the spheres, the sphere on

the right will have

A. no net charge. B. a positive charge. C. a negative charge.

Vector Fields – add vectors!

By definition: Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate).

Electric Dipole: a pair of two equal and opposite

charges q separated by a small distance L Dipole moment:

Example 21-9: electric field of a dipole

21-6: Charges in electric fields

By definition:

So:

Dipole may experience a torque:

And has a potential energy:

A conducting sphere with a net charge of q and mass m is suspended from the ceiling by a

light string. A uniform electric field, E, is applied vertically downward on the sphere.

The tension T in the string is ____ the weight mg.

A. less thanB. equal toC. greater

thanm q

E

T

A conducting sphere with a net charge of q=−1 C and mass m = 1 g is suspended

from the ceiling by a light string. A uniform electric field, E = 5000 N/C, is applied vertically downward on the sphere. The

tension T in the string is

A. 5 10−3 NB. 9.81 10−3 NC. 4.81 10−3 ND. 1.48 10−2 NE. zero

m q

E

T

21-60 A dipole of moment 0.50 e nm is placed in a

uniform electric field that has a magnitude of 4.0 × 104 N/C. What is the magnitude of the torque on the dipole when (a) the dipole is aligned with the electric field, (b) the dipole is transverse to (perpendicular to) the electric field, and (c) the direction of dipole makes an angle of 30° with the direction of electric field? (d) Defining the potential energy to be zero when the dipole is transverse to the electric field, find the potential energy of the dipole for the orientations specified in Parts (a) and (c).

A proton is moving horizontally north in an electric field that points

vertically upward. The electric force on the proton is

A. zero. B. upward. C. downward. D. to the west. E. to the east.

Three positive and equal charges Q1, Q2, and Q3 are at the corners of an equilateral triangle as shown. Point P is at the midpoint of the line between Q1 and Q3. The electric field at P is

A. zero. B. not zero and is directed along the line from

P to Q3. C. not zero and is directed along the line from

P to Q2. D. not zero and is directed along the line from

Q1 to Q2. E. not zero and is directed along the line from

P away from Q2.

21-57

An electron starts at the position shown in Figure 21-39 with an initial speed v0 = 5.00 × 106 m/s at 45° to the x axis. The electric field is in the +y direction and has a magnitude of 3.50 × 103 N/C The black lines in the figure are charged metal plates. On which plate and at what location will the electron strike?

More ExamplesMore Examples

21-74

Two point particles, each of mass m and charge q, are suspended from a common point by threads of length L. Each thread makes an angle θ with the vertical as shown in Figure 21-44. (a) Show that

where k is the Coulomb constant. (b) Find q if m = 10.0 g, L = 50.0 cm, and θ = 10.0°.

21-86 (simplified)21-86 (simplified)

In Millikan's experiment, an oil drop In Millikan's experiment, an oil drop of radius 1.64 mm and density 0.851 of radius 1.64 mm and density 0.851 g/cmg/cm33 is suspended in chamber C is suspended in chamber C when a downward electric field of when a downward electric field of 1.92 × 101.92 × 1055 N/C is applied. Find the N/C is applied. Find the charge on the drop, in terms of charge on the drop, in terms of ee. .

21-86 During the Millikan experiment used to determine the

charge on the electron, a charged polystyrene microsphere is released in still air in a known vertical electric field. The charged microsphere will accelerate in the direction of the net force until it reaches terminal speed. The charge on the microsphere is determined by measuring the terminal speed. During one such experiment, the microsphere has radius r = 5.50 × 107 m, and the field has a magnitude E = 6.00 × 104 N/C. The magnitude of the drag force on the sphere is given by FD = 6 πηrv, where v is the speed of the sphere and η is the viscosity of air Polystyrene has density 1.05 × 103 kg/m3. (a) If the electric field is pointing down and the polystyrene microsphere is rising with a terminal speed of 1.16 × 10-4 m/s, what is the charge on the sphere? (b) How many excess electrons are on the sphere? (c) If the direction of the electric field is reversed but its magnitude remains the same, what is the new terminal speed?

22-2022-20

The electric field of an electric dipole The electric field of an electric dipole along the dipole axis is approximated by along the dipole axis is approximated by Equation 22-8 and Equation 22-9, which Equation 22-8 and Equation 22-9, which result from the termination of the two result from the termination of the two binomial expansions shown just before binomial expansions shown just before those equations. If the expansions were those equations. If the expansions were carried out further, what would be the carried out further, what would be the next nonzero term in the expression for next nonzero term in the expression for the dipole's electric field along the the dipole's electric field along the dipole axis? dipole axis?