Question

Qa 2 A semi-infinite line of charge of charge per unit length 1 is placed on the positive î-axis. A semicircular arc of charge of radius a is joined to it at the origin, with its centre on the ġ-axis, at a distance a away, as shown. The total charge on the semicircle is Q. a. [5 points] Determine the electric field at a point i = yỹ (y > 0) due to the straight line. b. [3 points] Show that your answer to part a always points at the same angle relative to the ġ-axis. What is that angle? c. [5 points] Now determine the electric field due to the semicircular arc at the point i = aỹ. d. [2 points] What charge on the semicircle Q should we choose to make the total electric field at aỹ point only in the +ỳ direction?

Answer 1

(a) dey dE aeroport de dEx a²+x² dx 2 de = kda Ja²+x2) dq = tex. de = kda a²+x² kida a²+x² dEy de coso kada a a²+x² Jatx? em (kado da (@?+22;3h dey de sino ka a cx رعد - ) fatxt Ey= kan da (5) (a²+x") } da Kad Termostat (3) (artan}}

a terra let na dx= 1 asendad A - Ey kad q sei & dip (aase seech?k زل) kad د) Cosa do f KA [sin (1177 - R КА (5) Ex= ki 5 xda (-ê (a²+022) 34 a ten & a sei o lo dx = Kd (a tem & laseidda) (a seco you (-) R sind da Illo tâ [-cosa] Kl.cî Ilo

ni so ز ر ) خر؟ kha KA -> 45° angle (C) de=ado da. charge per unit length da ña dq=q de ña ♡ do =dxada ㅈ ach de = K da his de sing -ko do a² Ecoso (-5) de coso dEy = =k a coso do (-5) ara Ey=kQ coo do ts

k4 [since] 5 D } Ey= ax dEx de sino sinado E- ky sind do 띠 a²t - K9 [ - Conc 000 ㅉ K9 x오 dk 1 aR aa so 있K9 ( a2 지 () total electric field g t브 ( ) a²a gk a²k î ki K9 다. ㅋ 여름 p = ad