Physics 11 Chapter 20: Electric Fields and Forces

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1 Physics Chapte 0: Electic Fields and Foces Yesteday is not ous to ecove, but tomoow is ous to win o lose. Lyndon B. Johnson When I am anxious it is because I am living in the futue. When I am depessed it is because I am living in the past. Anonymous Eveyday is a good day; some ae just bette than othes. Autho unknown Reading: pages Outline: Chages and Foces stuctue of the atom (PowePoint) types of chage consevation of chage conductos and insulatos (PowePoint) ways of chaging an object (PowePoint) lightning (PowePoint) Coulomb s Law foce between two point chages foce on a point chage fom moe than one chage Electic Field definition electic field fom point chages Applications of the Electic Field electic field lines (PowePoint) electic shielding (PowePoint) Poblem Solving Many poblems in this chapte deal with Coulomb's law. Given two chages and thei sepaation, you should be able to calculate the foce (both magnitude and diection) each exets on the othe. You should know how to use vecto addition to find the esultant foce when moe than one chage inteacts with the chage of inteest. Vaiations include poblems that ask you to find one of the chages o the position of a chage, given the foce. To find the value of one o moe of the chages in some poblems, a peliminay calculation must be pefomed pio to using Coulomb's law. Fo example, you may need to calculate the total chage in an object. Remembe that chage is quantized and can only occu in multiples of e = C.

2 You should know how to compute the electic field of a collection of point chages. Remembe that the sum of the individual fields is a vecto sum. Add the x components to get the x component of the sum; add the y components to get the y component of the sum. The magnitude of the electic field poduced by a single point chage q, at a point a distance away, is given by E = k q /. This must be multiplied by the sine o cosine of an angle to obtain a component. You must also detemine the sign of the component. Some poblems deal with electic field lines. You should know that the electic field at any point is tangent to the line though that point, that the numbe of lines pe unit aea passing though an aea pependicula to the lines is popotional to the magnitude of the field, and that lines emanate fom positive chage and end at negative chage. You will also need to know that the magnitude of the foce on a chage in an electic field is given by the poduct of the chage and the electic field: F = qe. Fo a positive chage, the foce is in the same diection of the electic field, while fo a negative chage, it is in the opposite diection of the electic field. Questions and Example Poblems fom Chapte 0 Question The figue below shows fou situations in which chaged paticles ae fixed in place on an axis. In which situation(s) is thee a point to the left of the paticle whee an electon will be in equilibium? Question The figue to the ight shows fou situations in which paticles of chage +q o q ae fixed in place. In each, the paticles on the x-axis ae equidistant fom the y-axis. What is the diection of the net foce on the middle paticle in each case?

3 SUMMARY The goal of Chapte 0 has been to develop a basic undestanding of electic phenomena in tems of chages, foces, and fields. GENERAL PRINCIPLES Chage Thee ae two kinds of chages, called positive and negative. Atoms consist of a nucleus containing positively chaged potons suounded by a cloud of negatively chaged electons. The fundamental chage e is the magnitude of the chage on an electon o poton: e =.60 * 0-9 C. Matte with equal amounts of positive and negative chage is neutal. Chage is conseved; it can t be ceated o destoyed. Coulomb s Law The foces between two chaged paticles and sepaated by distance ae Kƒ F on = F on = q ƒƒq ƒ whee K = 8.99*0 9 N # m /C is the electostatic constant. These foces ae an action/eaction pai diected along the line joining the paticles. The foces ae epulsive fo two like chages, attactive fo two opposite chages. The net foce on a chage is the vecto sum of the foces fom all othe chages. The unit of chage is the coulomb (C). q F on q q q F on IMPORTANT CONCEPTS The Electic Field Chages inteact with each othe via the electic field. Chage A altes the space aound it by ceating an B electic field. A F on B The field is the agent that exets a foce F B on B = q on chage B. B E B An electic field is identified and measued in tems of the foce on a pobe chage q. E B = FB on q The unit of the electic field is N/C. q The electic field is a vecto. The electic field fom multiple chages is the vecto E B total = sum of the fields fom the individual E B + E B + chages. Á E Ḅ Visualizing the electic field The electic field exists at all points in space. An electic field vecto shows the field only at one point, the point at the tail of the vecto. Afield diagam shows field vectos at seveal points. Electic field lines: ae always paallel to the field vectos. ae close whee the field is stong, fa apat whee the field is weak. go fom positive to negative chages. APPLICATIONS Thee ae two types of mateial, insulatos and conductos. Chage emains fixed on an insulato. Chage moves easily though conductos. Chage is tansfeed by contact between objects. A dipole has no net chage, but has a field because the two chages ae sepaated. A dipole will otate to align with an electic field. E Electic fields: impotant cases The electic field of a point chage is Kƒ E B = a q ƒ fom q if q 7 0, caway towad q if q 6 0 db The electic field inside a paallel-plate capacito is unifom: E B = a Q, fom positive to negativeb P 0 A whee P 0 = 8.85 * 0 - C /N # m is the pemittivity constant. Conductos in electic fields The electic field inside a conducto in electostatic equilibium is zeo. Any excess chage is on the suface. The electic field is pependicula to the suface. The density of chage and the electic field ae highest nea a pointed end. E 5 0

4 Question 3 Dawings I and II show two examples of electic field lines. Decide which of the following statements ae tue and which ae false, defending you choice in each case. (a) In both I and II the electic field is the same eveywhee. (b) As you move fom left to ight in each case, the electic field becomes stonge. (c) The electic field in I is the same eveywhee but becomes stonge in II as you move fom left to ight. (d) The electic fields in both I and II could be ceated by negative chages located somewhee on the left and positive chages somewhee on the ight. (e) Both I and II aise fom a single positive point chage located somewhee on the left. Poblem A plate caies a chage of 3.0 µc, while a od caies a chage of +.0 µc. How many electons must be tansfeed fom the plate to the od, so that both objects have the same chage? Poblem The nucleus of the helium atom contains two potons that ae sepaated by about m. Find the magnitude of the electostatic foce that each poton exets on the othe. (The potons emain togethe in the nucleus because the epulsive electostatic foce is balanced by an attactive foce called the stong nuclea foce.)

5 Poblem 3 Given that q = + µc and d = 6 cm, find the diection and magnitude of the net electostatic foce exeted on chage q in the figue below. Poblem 4 A chage of 3.00 µc is fixed at the cente of a compass. Two additional chages ae fixed on the cicle of a compass (adius = 0.00 m). The chages on the cicle ae 4.00 µc at the position due noth and µc at the position due east. What is the magnitude and diection of the net electostatic foce acting on the chage at the cente? Specify the diection elative to due east.

6 Poblem 5 Thee point chages have equal magnitudes, to being positive and one negative. These chages ae fixed to the cones of an equilateal tiangle, as the dawing shows. The magnitude of each of the chages is 5.0 µc, and the lengths of the sides of the tiangle ae 3.0 cm. Calculate the magnitude of the net foce that each chaged expeiences.

7 Poblem 6 A tiny ball (mass = 0.0 kg) caies a chage of 8 µc. What electic field (magnitude and diection) is needed to cause the ball to float above the gound? Poblem 7 Two chages, -6 µc and +4.0 µc, ae fixed in place and sepaated by 3.0 m. (a) At what spot along a line though the chages is the net electic field zeo? Locate this spot elative to the positive chage. (b) What would be the foce on a chage of +4 µc placed at this spot?

Poblem 8 What ae the stength and diection of the electic field at the position indicated by the dot in the Figue below? Specify the diection as an angle above o below hoizontal.

8 Poblem 8 What ae the stength and diection of the electic field at the position indicated by the dot in the Figue below? Specify the diection as an angle above o below hoizontal. Poblem 9 A neutal conducting sphee is between two paallel chaged plates, as shown in the Figue below. Sketch the electic field lines in the egion between the plates. Be sue to include the effect of the conducting sphee.

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241 Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge