TAMU PHYS 208 - PHYS208_Exam1spring16-Solutions (9 pages)

208 Mid Term 1 POINTS TABLE Multiple Choice out of 20 Problem 1 out of 20 Problem 2 out of 20 Problem 3 out of 20 Problem 4 out of 20 TOTAL SCORE out of 100 v A lYS 0 1 MC 1 D MC 1 B C D E AC Li l LJY tv Cl D G v C 2 D MC3 B C 1 HCL B 1 20 marks A point charge q 80 0 nC is located at x y 2 00 m 1 00 m and a point charge q 2 60 0 nC is located at x y 0 00 2 00 m Determine the net electric field magnitude and direction at the origin of the x y coordinate system f c kA r 2 1 1 1 GOSS E S1vic i L F q 2 0 t l f x V L Cf 2 bo n 2 cos b1 1 C g Et I E l f cq 10 4 l9 SinS gol c 1V1 z S l N c 9x10 X 0 c l C Gf b 0 n i h l 2 5 wV i C t9 t y C t 4 c 135 c r l 2q t 1 c 2 4 0 t t Ji0 ti tJ rs ts 1 20 marks A point charge q 1 60 0 nC is located at x y 2 00 m 1 00 m and a point charge q2 80 0 nC is located at x y 0 00 2 00 m Determine the net electric field magnitude and direction at the origin of the x y coordinate system i a I 9 xJo 9 boV1C 2 l1s l YI rs creo lo c E 2 E2 C x 10 1 cnC fi5 l1SM 1 q x 10 1 CZSonC l t1 l 2 4 j Lt 3 Ye 30 Nfc o c lo 2 20 marks Charge Q is distributed evenly throughout the volume of an insulating sphere that has radius R Assume that the potential V O at r oo Calculate the potential at a radius of r R 3 J Q v o t r Q L t31TR21 E r 1n oK3 00 2 20 marks Charge Q is distributed evenly throughout the volume of an insulating sphere that has radius R Assume that the potential V O at r oo Calculate the potential at a radius of r R 2 Q j Q tt 3 rrR 3 f 4mr 2 f or Y L 1 41TY 2 a enc 3J J g e o G t 13 rr R 3 4 3 ln E 3 3 21 o R 3 20 marks A hollow but not necessarily empty conducting spherical shell has an inner radius of 8 00 cm and an outer radius of 10 0 cm There is an electric field at the inner surface of the shell Ei which has a magnitude of 80 0 N C and points toward the center of the sphere at all points on the inner surface The electric field at the outer surface of the shell E0 has a magnitude of 80 0 N C and points away from the center of the sphere as shown at all points on the outer surface Determine the magnitude of the charge on a the inner surface and b the outer surface of the spherical shell b lr i f 0 30 E Y o go 0 10 VV S Li ITY t x 10 11 C L L L Y 0 l V s id e 0 Q f i irri Q D Q e VlC Q C at y D Oo Jr Qi 0 LtTifo r2 2 g 0 E go ttn 0 ro x 10 11 C Q 0 N c Ltnu o lo Y z 15gq C J xn10 11 C 3 20 marks A hollow conducting spherical shell has an inner radius of 8 00 cm and an outer radius of 10 0 cm The electric field at the inner surface of the shell Ei has a magnitude of 40 0 N C and points toward the center of the sphere and the electric field at the outer surface E0 has a magnitude of 40 0 N C and points away from the center of the sphere as shown Determine the magnitude of the charge on a the inner surface and b the outer surface of the spherical shell D 0 10 for rL L VVl 0 lj lc w heV ch ci r e w i th c o vi o 5pher1 s e ti Q eN C y t nfo 2 o c o L n Eo o 08 YVt 2 ii 1 Y x c10 C 11 t L lfL in id e E o 33t t l L TIV 2 J Q enc Q l o f o QeY c Qv nc o t Qc x 10 11 C Q 0 G8 x 10 11 C 4 20 marks The electric potential inside a 10 m long linear particle accelerator is given by V 3000 Sx 2 m 2 V where xis the distance from the left plate along the accelerator tube as shown in the figure Proton a Determine an expression for the electric field along the accelerator tube b A proton is released from rest at x 4 m x Calculate the acceleration of the proton just after x Om x l Ill x Om it is released c What is the impact speed of the proton when and if it collides with the plate v b F V q c O t x 10 C 1 0 k 0 Ir 5N v j 0 x z ty 3 03 JO e e V c J C 1Jj L J wi A Iv v z A to th E w hu k l 2 Y 11 f u u 1 2 YY Vf 0 2 L 1 f 3000 5 x b s li v V 5 loo v l f 20 0 i 2 x JO 11 J 4 20 marks The electric potential inside a I 0 0 m long linear particle accelerator is given by V 2000 Sx 2 m 2 V where xis the distance from the left plate along the accelerator tube as shown in the figure Proton a Determine an expression for the electric field along the accelerator tube b A proton is released from rest at x 4 00 m Calculate the acceleration magnitude and r Om x tm x Om direction of the proton just after it is released c What is the impact speed of the proton when and it it collides with one of the end plates A Q J E l 6X 0 t t b l q x IO c l b 7 f Q Z I J 3 3 0 c J 9 o cce e rc ti 4 o the ef v 0 p1 e 0 vJ 6l 6 1 l lfLvv V Y V J t 0 1 i zooo t 5 x rvi 2 v i 5 …