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Physics 202 Electric Field

Transcript of Chapter 21 Electric Field I

The Electric Field I: discrete chargeChapter 21

2008 by W.H. Freeman and Company

Charges

Similar charges repel Opposite charge attract

Charge is quantized and conserved

Charge comes in little packets

The amount of charge is always conserved

21-21

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

Electric charges of the opposite signattract each other. B. exert no forces on each other. C. repel each other.A.

Experimental evidence indicates thatcharge is quantized and conserved. B. charge is quantized but not conserved. C. charge is conserved but not quantized. D. charge is neither quantized nor conserved.A.

How many electrons must be transferred to a body to produce a charge of 125 nC? 1.25 107 B. 1.60 1019 C. 1.28 1012 D. 3.45 1011 E. 7.81 1011A.

Three kinds of materials

Conductorsmaterials through which charge can move rather freely

Insulatorsmaterials through which charge cannot move freely

Note: These are RELATIVE categories

Charging by induction

Coulombs law

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

F in Newtons q in coulombs r in meters k is ???

Units

Units of k are empirical More realistic units are

21-26A point charge q1 = 4.0 C is at the origin and a point charge q2 = 6.0 C is on the x axis at x = 3.0 m. (a) Find the electric force on charge q2. (b) Find the electric force on q1. (c) How would your answers for Parts (a) and (b) differ if q2 were -6.0 C?

Superposition

Electrostatic forces like all forces - obey superposition Add vectorially use components

21-36

The structure of the NH3 molecule is approximately that of an equilateral tetrahedron, with three H+ ions forming the base and an N3ion at the apex of the tetrahedron. The length of each side is 1.64 10-10 m. Calculate the electric force that acts 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

39

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?

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. B. C.

no net charge. a positive charge. a negative charge.

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.B. C.

less than equal to greater thanE

T q m

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 isA.

B.C. D. E.

5 103 N 9.81 103 N 4.81 103 N 1.48 102 N zero

T q m E

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 isA. B. C. D. E.

zero. upward. downward. to the west. 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 isA. B.

C.

D.

E.

zero. not zero and is directed along the line from P to Q3. not zero and is directed along the line from P to Q2. not zero and is directed along the line from Q1 to Q2. 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 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 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 = 10.0.

21-86 (simplified)

In Millikan's experiment, an oil drop of radius 1.64 mm and density 0.851 g/cm3 is suspended in chamber C when a downward electric field of 1.92 105 N/C is applied. Find the charge on the drop, in terms of e.

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 rv, where v is the speed of the sphere and 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?

22-20

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