Physics 107 HOMEWORK ASSIGNMENT #15

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Physics 7 HOMEWORK SSIGNMENT #5 Cutnell & Johnson, 7 th eition Chapte 8: Poblem 4 Chapte 9: Poblems,, 5, 54 **4 small plastic with a mass of 6.5 x - kg an with a chage of.

1 Physics 7 HOMEWORK SSIGNMENT #5 Cutnell & Johnson, 7 th eition Chapte 8: Poblem 4 Chapte 9: Poblems,, 5, 54 **4 small plastic with a mass of 6.5 x - kg an with a chage of.5 µc is suspene fom an insulating thea an hangs between the plates of a capacito (see the awing). The is in euilibium, with the thea making an angle of. with espect to the vetical. The aea of each plate is.5 m. What is the magnitue of the chage on each plate? * Refe to Inteactive Solution 9. to eview one way in which this poblem can be solve. Two potons ae moving iectly towa one anothe. When they ae vey fa apat, thei initial spees ae. x 6 m/s. What is the istance of closest appoach? * ssm Detemine the electic potential enegy fo the aay of thee chages shown in the awing, elative to its value when the chages ae infinitely fa away. *5 ssm Euipotential suface has a potential of 565, while euipotential suface has a potential of 785. paticle has a mass of 5. x - kg an a chage of 4. x -5 C. The paticle has a spee of. m/s on suface. n outsie foce is applie to the paticle, an it moves to suface, aiving thee with a spee of. m/s. How much wok is one by the outsie foce in moving the paticle fom to? 54 The awing shows fou point chages. The value of is. µc, an the istance is.96 m. Fin the total potential at the location P. ssume that the potential of a point chage is zeo at infinity.

2 4. RESONING ND SOLUTION Since the thea makes an angle of. with the vetical, it can be seen that the electic foce on the, F e, an the gavitational foce, mg, ae elate by F e = mg tan. The foce F e is ue to the chage being in the electic fiel of the paallel plate capacito. That is, F e = E () whee is the magnitue of the 's chage an E is the magnitue of the fiel ue to the plates. ccoing to Euation 8.4 E is E = (8.4) ε whee is the magnitue of the chage on each plate an is the aea of each plate. Substituting Euation 8.4 into Euation () gives Solving fo yiels F e = mg tan. = ε ε mg tan. = ( ) ( )( )( ) 8.85 C / N m.5 m 6.5 kg 9.8 m/s tan. = 6.5 C 8 =.5 C. RESONING The only foce acting on each poton is the consevative electic foce. Theefoe, the total enegy (kinetic enegies plus electic potential enegy) is conseve at all points along the motion. Fo two points, an, the consevation of enegy is expesse as follows: EPE EPE = Initial kinetic enegies of the two potons Initial electic potential enegy Final kinetic enegies of the two potons Final electic potential enegy

3 The electic potential enegy of two potons (chage on each poton = e) that ae sepaate by a istance can be foun by combining the elations EPE = e (Euation 9.) an = ke/ (Euation 9.6) to give EPE = ke /. y using this expession fo EPE in the consevation of enegy elation, we will be able to etemine the istance of closest appoach. SOLUTION When the potons ae vey fa apat ( = ), so that EPE = J. t the istance of closest appoach, the spee of each poton is momentaily zeo (v = m/s). With these substitutions, the consevation of enegy euation euces to = ke Solving fo, the istance of closest appoach, gives 9 9 ( 8.99 N m / C )(.6 C) 7 6 (.67 kg)(. m/s) ke 4 = = =.5 m We have taken the mass of a poton fom the insie of the font cove of the text.. SSM RESONING Initially, the thee chages ae infinitely fa apat. We will pocee as in Example 8 by aing chages to the tiangle, one at a time, an etemining the electic potential enegy at each step. ccoing to Euation 9., the electic potential enegy EPE is the pouct of the chage an the electic potential at the spot whee the chage is place, EPE =. The total electic potential enegy of the goup is the sum of the enegies of each step in assembling the goup. SOLUTION Let the cones of the tiangle be numbee clockwise as, an, stating with the top cone. When the fist chage ( = 8. µc) is place at a cone, the chage has no electic potential enegy, EPE =. This is because the electic potential pouce by the othe two chages at cone is zeo, since they ae infinitely fa away. Once the 8.-µC chage is in place, the electic potential that it ceates at cone is = k whee = 5. m is the istance between cones an, an = 8. µc. When the.-µc chage is place at cone, its electic potential enegy EPE is

4 EPE k = = =. C =.88 J 5. m ( ) ( 9 )( N m /C 8. C ) 6 The electic potential at the emaining empty cone is the sum of the potentials ue to the two chages that ae aleay in place on cones an : k k = whee = 8. µc, =. m, =. µc, an = 4. m. When the thi chage ( = 5. µc) is place at cone, its electic potential enegy EPE is EPE k k = = = k 6 9 ( )( ) C. C = 5. C 8.99 N m /C =.4 J. m 4. m The electic potential enegy of the entie aay is given by EPE = EPE EPE EPE =.88 J (.4 J) =.746 J 5. SSM RESONING The total enegy of the paticle on the euipotential suface is E E =. Similaly, the total enegy of the paticle when it eaches euipotential suface is =. ccoing to Euation 6.8, the wok W one by the outsie foce is eual to the final total enegy E minus the initial total enegy E ; W E E =. SOLUTION The wok one by the outsie foce in moving the paticle fom to is, ( ) ( ) ( ) W = E E = = m v v ( ) = (5. kg) (. m/s) (. m/s) 5 [ ] (4. C) =. J

5 54. RESONING The electic potential at a istance fom a point chage is given by Euation 9.6 as = k /. The total electic potential at location P ue to the fou point chages is the algebaic sum of the iniviual potentials. SOLUTION The total electic potential at P is (see the awing) ( ) ( ) ( ) ( ) k k k k k = = P Substituting in the numbes gives ( ) ( ) 9 N m C k C = = = m

Physics 107 TUTORIAL ASSIGNMENT #8

Physics 107 TUTORIAL ASSIGNMENT #8 Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type