v o a y = = * Since H < 1m, the electron does not reach to the top plate.

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1 . The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the electon ech the top plte? Justi ou nswe b poviding numeicl dt. v o * m * ν ( ) ν ο ο m / s H H 0. 90m * Since H < m, the electon does not ech to the top plte.. Thee point chges, µc ech, e plced on thee cones o n euiltel tingle with side m. Wite the net electic ield t the middle point, in tems o unit vectos m * k k N C nd * cos0. k N C 4 * sin 0 6. k N C 0 *.4( k N C) i 6.0( k N C) j ˆ ˆ

2 . long non-conducting clinde with dius 0.5 m hs volume chge densit ρ -5 nc/m. Find the mgnitude o electic ield (in N/C) t distnce 0. m om its is. enc d ε ο d πl enc π L L d 9 ρ N.5 ε ο C 4. ve long line o chge hving uniom chge densit λ is t distnce o d 0.4 m om positive point chge (Q 4 µc) s shown in the igue. I the net electic ield t point is zeo, ind the vlue o λ (sign nd mgnitude). Q λ d 0. m (due to the chged b) must be upwd to cncel the downwd ield (due to Q). Thus, λ should hve positive vlue. Q k λ Q k λ o Q 0.m λ µ C m λ µ C m 5. solid bll o dius R hs uniom volume chge densit ρ nd poduces cetin electic ield with mgnitude t point, which is t distnce R om the bll s cente (ig.). I coe o dius R/ is emoved om the bll (ig.), the ield mgnitude t point chnges to. Wht is the tio /? R Fig. Fig. k k, 4 π R 4 π R ( R ). ρ ρ

3 6. oints ( m, 0 m) nd ( 6 m, m) e in uniom electic ield ) ) 00 ( N / C) i 500( N / C) j. Clculte the potentil dieence V V. X X V V 6 d dl d dl V V V. kv dl dl 7. Thee pticles with eul mss but dieent chge e elesed om thei positions shown below (Q - µc, 9 cm). Wht is the highest kinetic eneg the pticle with chge Q cn obtin? Q Q Q U i k kq 6 kq 9. J U K U K i i. 0 0 K K. J *Since the pticles hve the sme mss K Q K.7 J. lectic chge Q nc is distibuted unioml long thin od o length 4 cm, s shown in the igue. Tke the electic potentil to be zeo t ininit. Clculte the electic potentil t the oigin. Q k d d dv kλ.5 cm 4.0 cm d V kλ kλ ln V 9 ln. 4 kv cm d Q

4 ultiple-choice Questions. Two ininitel lge conducting pltes e positivel chged so tht the suce chge densit o is twice tht o (σ σ ). Which o the ollowing sttements is coect? Region Region Region σ σ ) The net electic ield in egion is zeo. b) The net electic ield in egions nd is zeo. c) The diections o net electic ield in egions nd e the sme. d) The mgnitudes o the net electic ield in egions nd e eul.. point chge o mss m nd chge Q nd nothe point chge o mss m nd chge Q e elesed on ictionless tble. I the chge Q hs n initil cceletion o, wht will be the initil cceletion o Q? ) b) c) / d) 4. The two metl sphees shown in the igue hng om nlon theds close to ech othe. The chge o one sphee is Q, nd the othe is unchged. I the sphees e elesed om est, which o the ollowing sttements is tue: ) The ttct, touch ech othe, nd st in touch. b) The ttct, touch ech othe, nd then epel c) The do not ttct o epel ech othe. d) The epel ech othe until the stop t gete distnce. 4. n empt cone is plced inside uniom electic ield s shown in the igue. The electic lu, Φ, pssing though the cuved suce (S ) o the cone is: R ) Zeo b) πr c) 4πR d) πr se suce S Cuved suce S

5 5. chged conducting spheicl shell with net chge o - hs dii nd b. I point chge o is plced t the cente, then the suce chge densit on the oute suce o the conducting shell is: ) Zeo b) /(4πb ) c) /(4πb ) d) -/(4πb ) b 6. Fou Closed suces S, S, S nd S 4 togethe with the chges Q, 5Q nd -Q e sketched s shown in the igue. I Q.5 pc then the net electic lu (in Nm /C) though the suce S is: S ) 0 b) c) d) 4 S Q S -Q 5Q S 4 7. The wok done b the electic ield to move chge Q om point to point long thee dieent pths with length L, L nd L is denoted b W, W nd W, espectivel. I L L L, then: ) W W W b) W.5 W c) W W W d) W W W L L L. conducting spheicl shell with inne dius nd oute dius b cies chge Q. The electic potentil (with espect to ininit) t the cente o the shell is: ) kq/(b-) b) Zeo c) kq/ d) kq/b b

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