lectic Chage and ield Chapte 6 (Giancoli) All sections ecept 6.0 (Gauss s law) Compaison between the lectic and the Gavitational foces Both have long ange, The electic chage of an object plas the same ole in detemining the electic foce as does the object s mass in the gavitational foce Both ae cental foces (foces act along the line joining the objects) But! Mass is alwas a positive uantit the gavitational foce is alwas an attactive foce. lectic chage can be positive o negative i.e. the electic foce can be attactive o epulsive A ve useful ule fo detemining the diection of the foce: Stength The electic foces eeted b one pat of an atom on anothe pat ae much stonge than thei gavitational attaction. i.e. o atomic/subatomic paticles, the gavitational foce is usuall neglected. (We shall see an eample late on) Like chages epel, unlike chages attact The law of consevation of chage Total amount of chage in an isolated sstem emains constant. One cannot ceate o desto a chage ample: The deca of the neuton. An isolated neuton decas in about 5 minutes. 0 0 n p e v (neuton) (poton) (electon) (neutino) (Total chage is zeo befoe and afte the deca) The lectonic Chage The magnitude of the smallest (elementa) fee chage is the chage on the electon o the poton. This chage is denoted b e. B convention: Chage on poton e Chage on electon e In the SI sstem, the unit of chage is the coulomb [C]. e.6 0-9 C
Coulomb s Law: Povides a desciption fo the electic foce. If two chages, and ae sepaated b a distance Putting these togethe, k the magnitude of the foce acting on an chage is popotional to the poduct of the two chages. ( ) It is also popotional to the invese suae of the distance between the chages. ( ) This is Coulomb s Law and gives the magnitude of the foce between two chaged paticles. k, the popotionalit constant, is given b k 8.990 9 Nm /C 90 9 Nm /C Sometimes it is moe convenient to wite: k whee ε 0 is the pemittivit of vacuum 4πk 4 π ε o ε 0 8. 85 0 C Νm If the two chages ae in a medium othe than vacuum, then k 4 π ε whee ε is the pemittivit of the medium One can also define the elative pemittivit, κ ε / ε 0, a dimensionless uantit, such that ε κ ε 0 ample: What is the foce acting on? magnitude: diection: k Attactive foce (unlike chages) ample: What is the foce acting on? Answe: Magnitude: k Diection: Attactive foce (unlike chages) Summa: The magnitude of the foce is given b Coulomb s Law, k Note: The magnitude of a vecto is alwas a positive uantit. Do not use the signs of the chages in this euation when calculating the magnitude of the foce. The diection of the foce is detemined fom Like chages epel, unlike chages attact
ample : Two fied chages, 3 µc and - 6 µc ae sepaated b 3 m. ind the electic foce (magnitude and diection) acting on. 3 µc -6 µc 3 m To find the diection of the foce, use the ule: like chages epel, unlike chages attact To find the magnitude, use Coulomb s Law. k 9 (9 0 N m / C )(3 0 (3 m).8 0 N 6 C)(6 0 6 C) (do not include the signs of the chages when using Coulomb s Law) What is the foce acting on? 3 µc -6 µc 3 m The magnitude of.8 0 - N ample : Compae the electic and gavitational foces between an electon of mass 9. 0-3 kg moving aound a poton of mass.67 0-7 kg in the H-atom at a distance of 0.05 0-9 m. m p.67 0-7 kg 0.05 nm m e 9. 0-3 kg The diection of is towad ample : Compae the electic and gavitational foces between an electon of mass 9. 0-3 kg moving aound a poton of mass.67 0-7 kg in the H-atom at a distance of 0.05 0-9 m. m p.67 0-7 kg e g e g 0.05 nm m e 9. 0-3 kg lectic oce: e k 9 9 9 (9 0 Nm / C )(.6 0 C)(.6 0 C) 9 (0.05 0 m) 8 9. 0 N Gavitational oce: g Gmm (6.67 0 7 Nm / kg )(.67 0 3 kg)(9. 0 9 (0.05 0 m) 47 4.05 0 N kg) 3
Theefoe, Hence, e >> g ; e / g.7 0 39 the electical foce is much stonge than the gavitational foce fo atomic paticles. g is neglected fo such paticles. What happens when thee ae moe than two chages pesent? How is Coulomb s Law applied? Use the supeposition pinciple The electic foce on a given chage is the vecto sum of the electic foces due to each chage Conceptual ample: What is the foce on? Conceptual ample: What is the foce on? 3 3 3 Conceptual ample: What is the foce on? ample : ind the electic foce acting on 3 3 3 3 0 cm Whee, 6 µc 4 µc 3 µc 3 3 Vecto Addition! 3 0 cm 3 0.0 m 3 (0.0 m) 4
3 3 0 cm 3 3 k3 (3) 9 (9 0.35 N Nm / C )(6 (0. 0 C)( m) 0 C) 0 cm The foces acting on 3 ae: 3 is the foce acting on 3 due to 3 is the foce acting on 3 due to 3 k3 (3) 9 (9 0.8 N Nm / C )(4 0 (0. m) C)( 0 C) Add 3 and 3 vectoiall to find 3 Diection of 3 : 3 3 () 3 ().35 cos 45 o 0 0.955 N 3 3 () 3 ().35 sin 45 o.8 N.75 N 0 cm 3 3 3. 9 N 3 3 3 0 cm 3 () 3 () tan θ 3 3.88 0 cm 3 θ 7 3 (measued fom the -ais) θ 0 cm 3 3 lectic ields Conside the space suounding a chage. An chage placed in that space will epeience an electic foce. 3 3 The electic field is a popet of the chage. The chage, which is used in detemining the electic field is called a test chage. B convention it is a positive chage. The test chage is not a eal chage. We use it onl to detemine the diection of the electic field. We can calculate the electic foce acting on at an point in space. The collection of all these foce vectos is the electic field ceated b a chage. 5
Definition of the lectic ield Define the magnitude of the electic field,, at a distance fom a point chage, as the foce on the test chage at that point divided b the value of the test chage. k k Units fo : N/C This is the magnitude of the -field ceated b the chage. The diection of is the diection of the foce acting on the positive test chage at that point. If we know the -field at a point, then if a chage is placed at that point it will epeience an electic foce given b Note that the -field is not poduced b '. If is a positive chage, the diection of the foce acting on it will be in the same diection as the -field at that point. If is a negative chage, the diection of the foce acting on it will be in the opposite diection fom the the -field at that point. ample : Thee chages ae positioned at 3 of the 4 cones of a suae of side 0 cm. ach have a chage of 5 0-0 C. Calculate the -field at the empt cone. 0 cm 3 ample : Thee chages ae positioned at 3 of the 4 cones of a suae of side 0 cm. ach have a chage of 5 0-0 C. Calculate the -field at the empt cone. ample : Thee chages ae positioned at 3 of the 4 cones of a suae of side 0 cm. ach have a chage of 5 0-0 C. Calculate the -field at the empt cone. 3 0 cm 3 o moe than one chage use the supeposition pinciple: 3 o moe than one chage use the supeposition pinciple: 3 3 0 cm 3 6
Magnitudes: 3 k k k3 3 9 0 (9 0 N m / C )(5 0 C) (0. m) 9 0 (9 0 N m / C )(5 0 C) (0. m) 9 0 (9 0 N m / C )(5 0 C) (0. m) 450 N / C 5 N / C 450 N / C cos 450 N/C (5 N/C) (0.707) 608 N/C 3 sin 450 5 (0.707) 608 N/C 3 0 cm 3 Theefoe, the magnitude is; And the diection is; tan θ θ 45 86 N / C 3 3 0 cm 3 If a chage of -5 X 0-0 C is placed at the 4 th cone, what will be the electic foce acting on this chage? 4-4 0 cm 3 The magnitude of (5 0-0 C)(86 N/C) 4.3 0-7 N The diection of is opposite to because 4 is negative 7