JJ 5 H Physics (646) Electic Fields_tutsoln JURONG JUNIOR COLLEGE Physics Depatment Tutoial: Electic Fields (solutions) No Solution LO Electic field stength at a point in an electic field is defined as the foce pe unit positive chage acting on a small chage placed at that point. The electic potential at a point in an electic field is defined as the wok done pe unit positive chage (by an etenal agent) in binging a small chage fom infinity to that point. (a) (h) dv E, (ii) d du F d a) (b) b) 3 a) E A, E B (c) (d) Physics Dept Page of 6
JJ 5 H Physics (646) Electic Fields_tutsoln b) c) d) e) f) g) F V A U V B U + V + πε h) and ae point chages; The sepaation between the chages is much lage than the dimensions of the chages; The chages ae unifomly distibuted on the object sufaces. 4 a) In tems of magnitude, ( ) E +C E -C () ( ) NC - ( ) ( ) E +C E -C () 4 ( ) NC - ( ) (d) In tems of diection, E +C and E -C ae in the same diection towads C hence the esultant A is 6 ( ) NC - ( Pointing to the ight of pape) In tems of diection, E +C and E -C ae in the same diection towads C hence the esultant B is 6 ( ) NC - ( Pointing South East) The vetical components of esultant of A and B will cancel off each othe. Hence the esultant electic field stength is the adding of the hoizontal components of esultant A and B 6( )cos 45 + 6( )cos 45 7.64 NC - ( to the ight.) b) ( )( + ) ( )( ) ( )() ( )( ) + + +.5.5.5.5 J C - Physics Dept Page of 6
JJ 5 H Physics (646) Electic Fields_tutsoln 5 Both ae invese squae law fields. Electic field is geneated by a chage. Gavitational field is geneated by a mass. Electic field eets a foce on a chage. Gavitational field eets a foce on a mass. Unifom electic field is set up by paallel chaged plates (ecept nea edges). Nea the suface of the Eath, gavitational field is appoimately unifom. Electic field stength is dependent on the medium it is in. Gavitational field stength is independent on the medium it is in. (k) 6 Electic field stength at the fouth cone due to the two + chages ae E and E, with magnitude. πε 4 o E4 is the esultant of E and E, hence E4. o Electic field stength due to the chage is E3 4 πεo( ) Since E3 is less than E4, answe is B. 8πε o. (d) E4 E E E3 7 Along XY, the electic foce is pependicula to the path XY, hence wok done against electic foce is zeo. (f) 8 Along YZ, the component of E along YZ is E sin6. Hence, wok done against electic foce along YZ fo a unit positive chage is Es sin6 (Negative as the motion YZ is not against the electic foce, the motion is in the diection of the electic foce.). Along ZX, the component of E along ZX is E sin6. Hence, wok done against electic foce along ZX fo a unit positive chage is Es sin6. 6.5 Foce gadient of gaph 7.5-5 N. F qe q V d (5. 4-6 )..5 - N 6 Potential at cente of cicle V sum of potential due to individual chages o Wok done by an etenal agent to move chage fom infinity to cente of cicle wok done by epulsive foces to move fom cente of cicle to infinity 6 6 V o o (f) (f) (h) Physics Dept Page 3 of 6
JJ 5 H Physics (646) Electic Fields_tutsoln Mass of poton u (u.66-7 kg) Chage on poton e Mass of α-paticle 4 u Chage on α-paticle e Gain in K.E. loss in P.E. mv qv Fo poton, (u)v ev - - - - - () Fo α-paticle, α ev - - - - - () () () : 4v v α v α v (g) ΔKE ΔPE mv qδv q 4 πεo.. q o () (. -5 )v (.5 - )( )(. -4 )() v m s - 3 (a) Hoizontally, using s u t, s time inteval that the electon is inside the electic field t 5. - s (b) Vetically, ma qe e V d 4 m s - u. a ev md (. 6 )( 5) 8.78 3 (. )( 5. ) 7 (g) (e) (c) Using s y u y t + a yt, s y a yt ev md s u (. 6 )( 5). 3 7 (. )( 5. ).. m (d) The diection of the electic field stength (high V to low V): downwads. The diection of the electic foce acting on a electon ( ve): upwads. (e) Taking upwads positive and bottom plate as efeence F/N 8. -6 5 /cm Physics Dept Page 4 of 6
JJ 5 H Physics (646) Electic Fields_tutsoln (ii) Taking upwads positive and bottom plate as efeence V/V 5 (iii) 5 /cm Taking upwads positive and bottom plate as efeence E/ V m - 5 /cm -5 4 ai aii aiii Physics Dept Page 5 of 6
JJ 5 H Physics (646) Electic Fields_tutsoln b c Physics Dept Page 6 of 6