Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)

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1 Geneal physics II (10) D. Iyad D. Iyad Chapte : lectic Fields In this chapte we will cove The lectic Field lectic Field Lines -: The lectic Field () lectic field exists in a egion of space suounding a chaged object. If anothe chaged object entes a egion whee an electical field is pesent it will be subject to an electical foce. Assume a small +ve test chage q 0 is placed at point P in the electic field of positively chaged object lectic Field due to point chage lectic Field due to a Continuous Chage Distibution Motion of a Chaged Paticle in a Unifom lectic Field A Dipole in an lectic field The diection of at point P will be the same diection of the foce exceted on the test chage q 0 placed at point P F -1: What is physics? In pevious chapte, we discussed the electic foce on chaged paticles when they placed nea each othe; The will be attaction o epulsion between the chages exist in the system. The Question is: How do any chage feel the pesence of othe chage without touching each othe? The answe: Any chaged paticle 1 set up an electic field in the space suounding itself. If we place othe chaged paticle at any given point in that space, paticle 1 knows of the pesence of second paticle because paticle is affected by the electic field exist at that point fom paticle 1. paticle 1 pushes o pulls on paticle not by touching it but by means of the electic field poduced by paticle 1. Ou goal in this chapte is to define electic field and discuss how to calculate it fo vaious aangements of chaged paticles. -: The lectic Field () Diection defined as the diection of the electical foce exeted on a small +ve chage (q 0 ) placed at that location. +Q -Q q 0 lectic field points away fom a +ve chage The electic field is geneally changes with position (location) The electic field is vecto quantity : magnitude and diection. q 0 lectic Field points towads a -ve chage

2 Geneal physics II (10) D. Iyad -: The lectic Field () Hence, the electic field is defined by the electic foce exeted on a small chaged paticle (q 0 ) fom an othe chaged object. = F q 0 magnitude of electic field is = F q 0 ( SI unit is N/C) F -: lectic Field Lines Remaks continued: Field lines stat fom positive chages an end at negative ones. Numbe of lines leaving (o appoaching) the chage is popotional to the magnitude of the chage Field lines can not coss. xamples on -field lines: 1) lectic field lines of single positive (a) and negative (b) chages. With diection same as foce diection acting on small +ve test chage q 0 -: lectic Field Lines A convenient way to visualize electic field pattens is to daw lines in the diection of the electic field. Such lines ae called electic field lines. Remaks: lectic field vecto,, is tangent to the electic field lines at each point in space. The numbe of lines pe unit aea though a suface pependicula to the lines is popotional to the stength of the electic field in a given egion. is lage when the field lines ae close togethe and small when fa apat. nea the sphee > fa away fom the sphee -: lectic Field Lines ) two point chages two simila chages of equal magnitude ( A > B > C =0) Dipole: two opposite chages of equal magnitude two opposite chages of diffeent magnitude: numbe of lines leaving +q > numbe of lines enteing -q

3 Geneal physics II (10) D. Iyad -: lectic Field Lines ) plates -4: The lectic Field due to a point chage: xample x: A chage q 1 = 7 µc is located at the oigin, and a second chage q =-.0 µc is located on the x axis, 0. m fom the oigin. Find the electic field at the point P, which has coodinates (0, 0.4) m. Positively chaged plate: -field lines away fom plate negatively chaged plate: -field lines towads plate two oppositly chage plates: paallel lines -field away fom +ve plate towads ve plate -4: The lectic Field due to a point chage To find the electic field due to a point chage q (o chaged paticle) at any point a distance fom chage q, we put a positive test chage q 0 at that point; Calculate fom F F q qq0 = = k ˆ whee F = k ˆ q0 q with -field magnitude = k If q is +ve is diected away fom q If q is +ve is diected towads q Fo a goupe of chages, to find the -field at point P, we can use the supeposition pinciple (vecto sum of -fields fo all chages) = i = i = k i i i i q We can calculate the vectos of -fields 1 = (.9 10 ˆ) j N / C = cosθ iˆ sinθ ˆj 4 = ( )ˆ i ( ) ˆj ( iˆ = ˆ) j N / C -4: The lectic Field due to a point chage: xample continued fom pevious slide hence the total field at P is iˆ ˆ x y j ( iˆ = 1 + = + = ˆ) j N / C The magnitude: The diection: = x + y =.7 10 N / C = tan 1 y φ = 66 x

4 Geneal physics II (10) D. Iyad -4: The lectic Field due to an lectic Dipole An electic dipole: two chages of same magnitude and opposite signs (q and q) sepaated by a distance d. Fo the dipole shown, we can calculate -field, along dipole axis, at point P (at distance z fom dipole cente). Since we have point chages q q q q ( + ) = k = k and ( ) = k = k ( z d ) ( z + d ) ( + ) ( ) The total -field at P is the vecto sum q q = ( + ) + ( ) = k k in the z - diection ( z d ) ( z + d ) kq 1 1 in the z - diection (1 ) (1 ) = z d + d z z foming a common denominato -4: The lectic Field due to an lectic Dipole The -field due to an electic dipole at point P that lie on axis pass though the dipole cente and vetical to dipole axis can be calculated using same method q q ( + ) = ( ) = k = k, Because = ( + ) ( z + d / ( + ) the z - components of ( + ) and ( ) Hence, - field is on x - axis only Fo z>>d/ z + (d/) z ( d / ) z + ( d / ) ( ) ) 1 ( ) = ( + ) cosθ + ( ) cosθ = ( + ) cosθ q = k z + d cancels -4: The lectic Field due to an lectic Dipole Fo fa distance z z>>d/ d/z 0 Whee p = qd is the magnitude of electic dipole moment vecto p p is a vecto that is always diected fom - ve chage to + ve chage -4: The lectic Field due to an lectic Dipole: xample In the lectic dipole of pevious slide, if the electic dipole has a chage magnitude of µc and it is sepeated be cm. what is the electic foce on a test chage, q 1 = µc, located at point P (0 cm fom the dipole cente)? z>>d/ p = k z q1 p q1qd F = q1 = k = k z z F = ( 10 )( 10 )( 10 ) - (0 10 ) - = N in the diection of ( x-diection) - F = ( iˆ) N

5 Geneal physics II (10) D. Iyad -4: - Field due to an lectic Dipole: xample - lectic dipole and atmospheic spites عاصفة ( thundestom Spites ae huge flashes that occu fa above a lage occus (برق) They poduced when especially poweful lightning.(رعدية between the gound and stom clouds. This is due to -field aising fom electic dipole of eath and cloud. The -field at high atmosphee coss citical value ( c ) and hence motion of electons between atoms ionization light occus in (اشباح) shapes of Spites (برق) When lightning occus, Lage amount of ve chage (-q) tansfeed fom gound to the cloud +ve chage (+q) on eath lectic Field of a continuous chage distibution If we have a continuous chage distibution as shown We can choose an abitay element chage q (faction of total chage q) the -field ( - faction of total -field) due to q at point P located at is The total -field due to all chage element q i at P is appoximately -4: - Field due to an lectic Dipole: xample - lectic dipole and atmospheic spites continued fom pevious slide by assuming a vetical electic dipole that has chage -q at cloud height h and chage +q at below-gound depth h. If q =00 C and h =6 km, what is the magnitude of the dipole s electic field at altitude z 1 =0 km fom gound somewhat above the clouds) and altitude z =60 km (somewhat above the statosphee)? p qd 4qh = k = k = k z z z * At z=0 km = 0000 m = N/C at this hight, < c no spite will occu * At z=60 km = m = 10 N/C at this altitude, > c ionization of atoms will occue spites will occu lectic Field of a continuous chage distibution Fo chage elements appoaching zeo ( q i 0 q i dq ) we will have a continuous distibution fo chage q the total field at P is dq o the -field poduced at P by dq is Note that o is a vecto in the adial diection ( ) it may have components when consideing othe coodinate system like Catesian (xyz) coodinate system.

6 Geneal physics II (10) D. Iyad lectic Field of a continuous chage distibution To pefom integal calculations, it is useful to use the concept of chage density Q = ρv dq = ρdv Q = σa dq = σda -6: lectic Field due to a line chage: chaged ing x: A ing of adius R and unifom chage density λ. Calculate the electic field due to the ing at a point P lying a distance z fom its cente along the cental axis pependicula to the plane of the ing (x-y plane). 1) Fo sigment length (ac ds) the -field ( ) has two components: and ) If we chose othe segment length ds in font of fist one as shown components fom both segments cancels only z-components add Q = λl dq = λdl Paallel to z-axis pependicula to z-axis -6: lectic Field due to a line chage: chaged ode x: A od of length l has a chage density λ and a total chage Q. Calculate the electic field at a point P that is located along the long axis of the od and a distance a fom one end: Fo chage segment dq we have -field Since has only one component in the ve x-diection The magnitude of is -6: lectic Field due to a line chage: chaged ing continued fom pevious slide Fo all the ing, the pependicula components of the -field cancel We will only have z - component fo the -field z - component with Hence, and But In the z - diection

7 Geneal physics II (10) D. Iyad -6: lectic Field due to a line chage: chaged ing continued fom pevious slide -6: lectic Field due to a line chage: chaged ac - continued The -Field in the x-diection fo the ac is: Integate both sides πr is the cicumfeence (length) of the ing λ(πr) = q Note that the ac length ds = dθ In the z - diection (pependicula to ing x-y plane) -6: lectic Field due to a line chage: chaged ac x: A plastic od having a unifomly distibuted chage - Q. The od has been bent in a 10 cicula ac of adius as shown. In tems of Q and. what is the electic field due to the od at point P (at the oigin - cente of the ac)? We can choose othe symmetic element ds d y cancels and d x add as shown. -7: lectic Field due to a line chage: Chaged disk x: A disk of adius R and unifom chage density σ. Calculate the electic field due to the disk at a point P lying a distance z fom its cente along the cental axis pependicula to the plane of the ing (x-y plane). 1) We can choose a chage element to be a ing of adius aea da = πd dq = σda = σ (πd) ) The -field due to the ing of chage dq is We only have x-components fo the -field

8 Geneal physics II (10) D. Iyad -7: lectic Field due to a line chage: Chaged disk continued fom pevious slide Integate fo the vaiable (fom 0 - R) -8: A Point Chage In an lectic Field: xample: Chaged paticle in an -field x: A positive point chage q of mass m is eleased fom est, nea the +ve plate, in a unifom electic field diected as shown. Find the speed of the paticle when eaching ve plate. It can be integated with the help of integal ule: Solve the limits and eaange O othe solution -8: A Point Chage In an lectic Field When a paticle of chage q and mass m is placed in -field an electic foce F e will exet on the paticle causing it to acceleate -Field Foce F = q Using Newtom nd law Acceleation F q a = = m m -8: A Point Chage In an lectic Field: xample: Chaged paticle in an -field x: acceleated electon: An electon entes the egion of a unifom electic field as shown, with v i = 10 6 m/s and = 00 N/C. The hoizontal length of the plates is l = 0.1 m. Find a) the acceleation of the electon while it is in the electic field. b) If the electon entes the field at time t = 0, find the time at which it leaves the field c) If the electon position as it entes the field is (0,0), what is its vetical position when it leaves the field If -field is unifom a is constant equation of motion fo constant a (geneal physics 1) if q is +ve acceleation will have same diection of -field paticle will move in the diection of -field if q is -ve acceleation will have opposite diection of -field paticle will move in the opposite diection of -field

9 Geneal physics II (10) D. Iyad No foce in x-diection v x v a) b) In the x-diection x x = vxt t = = v c) -8: A Point Chage In an lectic Field: xample: continued fom pevious 1 y = viyt + a t x y l v x = i 1 e = 0 t m = constant no acceleation in x-diection (Acceleating downwad) -9: lectic dipole in an electic field When a dipole is placed in unifom electic field electic foce F = q will exet on both chages on diffeent diections net foce on the dipole = 0. But net foce poduces a net toque τ because foces acts on (عزم دوران) diffeent lines of action about thei cente of mass. d fo each chage τ = F sinθ = q sinθ total toque on both chages (dipole)is τ = qd sinθ p sinθ tot = net toque can be expessed as -9: lectic dipole in an electic field In mateial, electons and potons ae connected by an electic foce foming electic dipoles within the mateial like the wate o dielectic mateials. If you conside an electic dipole with distance d between them an electic dipole moment p exist (عزم قطبي آهرباي ي) between them whee p = p = qd p is a vecto diected fom q to + q -9: lectic dipole in an electic field since -foce is consevative and hence it s wok stoe potential enegy Rotation of dipole stoe a potential enegy within dipole. The dipole has its least potential enegy (U = 0) when its moment p is lined up ( ) with the field (when the angle θ is 90 ). The potential enegy U of the dipole at any othe value of θ can be found by calculating the wok W done by the field on the dipole when the dipole is otated to that value of θ fom 90. W = W = U = U U = 0 U C and = U Which (wok done on dipole by -field) can be expesed as i f f

10 Geneal physics II (10) D. Iyad -9: lectic dipole in an electic field: xample A neutal H O molecule has an electic dipole moment C.m. (a) How fa apat ae the molecule s centes of positive and negative chage? (b) If it is placed in an -field of N/C, what maximum toque can the field exet on it? (c) How much wok must an extenal agent do to otate this molecule by 180 in this field, stating fom aligned position, fo which θ = 0? Solution: (a) 10 electons and 10 potons exist in a neutal wate molecule (b) Maximum toque is when the angle between and p (c) Summay lectic Field is foce pe unit chage. Chages ae the souces of the -field. -field of a chage has diection same as foce diection on othe +ve chage Field lines help us visualize field diection and stength. Chages unde electic foce will acceleate lectic dipole will have a net toque unde the effect of extenal -field and hence it will stoe potential enegy