Physics 10 Jonthn Dowling Physics 10 ecture 9 FIRST MIDTERM REVIEW
A few concepts: electric force, field nd potentil Electric force: Wht is the force on chrge produced by other chrges? Wht is the force on chrge when immersed in n electric field? Electric field: Wht is the electric field produced by system of chrges? (Severl point chrges, or continuous distribution) Electric potentil: Wht is the potentil produced by system of chrges? (Severl point chrges, or continuous distribution)
Plus few other items Electric field lines, equipotentil surfces: lines go from +ve to ve chrges; lines re perpendiculr to equipotentils; lines (nd equipotentils) never cross ech other Guss lw: Φ=q/ε 0. Given the field, wht is the chrge enclosed? Given the chrges, wht is the flux? Use it to deduce formuls for electric field. Electric dipoles: field nd potentil produced BY dipole, torque ON dipole by n electric field, potentil energy of dipole Electric potentil, work nd potentil energy: work to bring chrge somewhere is W = qv (signs!). Potentil energy of system = negtive work done to build it. Conductors: field nd potentil inside conductors, nd on the surfce. Shell theorem: systems with sphericl symmetry cn be thought of s single point chrge (but how much chrge?) Symmetry, nd infinite systems.
Conductors nd insultors Will two chrged objects ttrct or repel? Cn chrged object ttrct or repel n unchrged object? Wht is the electric field inside conductor? Wht is the direction of the electric field on the surfce of conductor? Wht hppens to conductor when it is immersed in n electric field?
Electric forces nd fields: point chrges Figure N-14 shows n rrngement of four chrged prticles, with ngle θ = 34 nd distnce d =.0 cm. The two negtively chrged prticles on the y xis re electrons tht re fixed in plce; the prticle t the right hs chrge q = +5e () Find distnce D such tht the net force on the prticle t the left, due to the three other prticles, is zero. (b) If the two electrons were moved further from the x xis, would the required vlue of D be greter thn, less thn, or the sme s in prt ()? Other possible questions: wht s the electric field produced by the chrges XXX t point PPP? wht s the electric potentil produced by the chrges XXX t point PPP? Wht s the potentil energy of this system?
Electric dipoles Wht s the electric field t the center of the dipole? On xis? On the bisector? fr wy? Wht is the force on dipole in uniform field? Wht is the torque on dipole in uniform field? Wht is the potentil energy of dipole in uniform field?
Electric fields of distributed chrges Possible problems, questions: Wht s the electric field t the center of chrged circle? Wht s the electric field t the center of ¼ of chrged circle? Wht s the electric field fr from the ring? fr from the disk? Wht s the electric field of n infinite disk?
Guss lw A long, non conducting, solid cylinder of rdius 4.1 cm hs nonuniform volume chrge density tht is function of the rdil distnce r from the xis of the cylinder, s given by ρ = Ar, with A =.3 µc/m 5. () Wht is the mgnitude of the electric field t rdil distnce of 3.1 cm from the xis of the cylinder? (b) Wht is the mgnitude of the electric field t rdil distnce of 5.1 cm from the xis of the cylinder?
Guss lw At ech point on the surfce of the cube shown in Fig. 4-6, the electric field is in the z direction. The length of ech edge of the cube is.3 m. On the top surfce of the cube E = -38 k N/C, nd on the bottom fce of the cube E = +11 k N/C. Determine the net chrge contined within the cube. [-.9e-09] C
Guss lw: pplictions
Electric potentil, electric potentil energy, work In Fig. 5-39, point P is t the center of the rectngle. With V = 0 t infinity, wht is the net electric potentil in terms of q/d t P due to the six chrged prticles?
The figure shows conducting pltes with re A=1m, nd the potentil on ech plte. Assume you re fr from the edges of the pltes. Wht is the electric field between the pltes in ech cse? Wht (nd where) is the chrge density on the pltes in cse (1)? Wht hppens to n electron relesed midwy between the pltes in cse (1)?
Derive n expression in terms of q / for the work required to set up the fourchrge configurtion of Fig. 5-50, ssuming the chrges re initilly infinitely fr prt. The electric potentil t points in n xy plne is given by V = (.0 V/m )x - (4.0 V/m )y. Wht re the mgnitude nd direction of the electric field t point (3.0 m, 3.0 m)?
Exm Review Continued Questions: from checkpoints nd questions in the textbook! U = 5U 0, 7U 0, +3U 0, +5U 0
Problem Clculte electric field t point P. x dx P E Field very fr wy?
Potentil of Continuous Chrge Distribution Uniformly chrged rod Totl chrge Q ength Wht is V t position P shown? V! = Q / dq =! dx = kdq k# dx! =! r ( + " 0 x) x P = " [! ln( +! x ] k ) 0 dx V = & + k' ln $% #!"
Problem Field t center of rc?
ine Of Chrge: Field on bisector dx d P! x o de Chrge per unit length Q de = k( dq) d! = Distnce d = + x q de y = de cos" = ( + cos! = ( + k(! dx) x ) x 1/ ) 3/
ine Of Chrge: Field on bisector ine Of Chrge: Field on bisector! " + = / / 3/ ) ( y x dx k E # Wht is E very fr wy from the line (<<)? 4 k + =! / / x x k! " # $ % & ' + = ( k k E y!! = = E y ~kλ/()=kλ/ =kq/ Wht is E if the line is infinitely long ( >> )?
Problem: Guss w to Find E
Guss w: Cylindricl Symmetry Approximte s infinitely long line E rdites outwrds. Choose cylindricl surfce of rdius R, length co-xil with line of chrge. " = E A = E! R # = q =! " 0! 0 E =! "# R 0 =! "# 0 R R = 1 mm E =? 1 m! = k R
Potentil Energy of System of Chrges
Potentil Energy of A System of Chrges 4 point chrges (ech +Q) re connected by strings, forming squre of side If ll four strings suddenly snp, wht is the kinetic energy of ech chrge when they re very fr prt? Use conservtion of energy: Finl kinetic energy of ll four chrges = initil potentil energy stored = energy required to ssemble the system of chrges +Q +Q +Q +Q Do this from scrtch! Don t memorize the formul in the book! We will chnge the numbers!!!
Potentil Energy of A System of No energy needed to bring in first chrge: U 1 =0 Energy needed to bring in nd chrge: Chrges: Solution U = QV = 1 Energy needed to bring in 3rd chrge = kq U3 = QV = Q( V1 + V ) = + kq Energy needed to bring in 4th chrge = kq U 4 = QV = Q( V1 + V + V3 ) = + kq kq +Q +Q +Q +Q Totl potentil energy is sum of ll the individul terms shown on left hnd side = kq ( 4 + ) So, finl kinetic energy of ech chrge = kq 4 ( 4 + )
Electric fields: Exmple Clculte the mgnitude nd direction of the electric field produced by ring of chrge Q nd rdius R, t distnce z on its xis.
Smple Problem Figure N-14 shows n rrngement of four chrged prticles, with ngle θ = 34 nd distnce d =.0 cm. The two negtively chrged prticles on the y xis re electrons tht re fixed in plce; the prticle t the right hs chrge q = +5e ()Find distnce D such tht the net force on the prticle t the left, due to the three other prticles, is zero. (b) If the two electrons were moved further from the x xis, would the required vlue of D be greter thn, less thn, or the sme s in prt ()?