Question

Let a Point charge Q1 = 25nC be located at p1(4,-2, 7)and a charge Q2 = 60nC be at p2(-3, 4,-2). In the free space of Cartesian coordinate system. = Find: a) E at P3(1,2,3). b) E at the origin point. c) At what point on the y axis (0, y, 0) is E = 0.

Answer 1

Electric field in vector form: we have to calculate the +9 Electric field at the point P due to charge placed at the ri point 1. The position vector joining the point P be rp Tp and point 1 be ri. ri+ř = rp ř ř=ro- ri = rip, h = = rp - ří |rp – řil r

Q Q Ep = 41768r2' Î = E1p = 41€or2 a rp - 4160 lrp – řil Ep = e řip 41€ 1ř1p13

špi= 3p-n - 2 Now in given question't Q=81=288109 and pornit in Piri = 4î-27+7h @ Yewaan cwrite as spi=42-29 +22 8p=pornit P3 as bonilp = rp= 1[2] +3 ê Now Electric field at 3 due PII- E391 - Electric field at 3 due to l. šp-ñ = rî +27 +34-(41-21 +72) zête Î-4 Irpilad (3727 42+44)2 da+16+16 JAL = -38 +41 -4 41 fp = 25x109x9x18 (-3?tag-AE 225 C-32+49-4k Smllarfieldorfz due charge at 2. 82=8= Gonez Gonionc 82= asê +47 2k;8p= 45-23 +7 h 8p2 = 86-82=77-67+qk 17p2l= 72+6)2+0)2 2279 +36+81 Qs 4TG 18P2P fe E3-12 o х ATIG Irpl" 2 41 त41 MIC 흐 EP2a - 1166 8p2 Ipal

166 -sk Epsi 60x109x9x19 x 70-65+92 1166 Netfield at at P3 Ep3 - Ē3+ + [372 = For CZ2-6119€)+2={site? Electic at orign!- r r = 0 Ēo at crigni net field smllanily. Epa 45+23 7k Fotopi = -4+29-76 4T (1692 169 Toile J24) 2 +@1772 - 225 x =/16+4+49 69 169 Now field due to charge P2! Ēo due to R2 = 8zc (+38-41 +22] 41764d (3)2+(4)2422) 3²(4)+22 (30-47 +2k d29) 2 29 ec zî -47 +2k NIC 29 d2q Metfield Boz koupit Boxes 2 (4 -7 +7 = 169 (-tai-) Me - =640 2 540 z = 225 6769 As

3312 -73-5= -4 î+ ATIG Told [4)2+(4-2)2 Now the post on the yaxio considerat ap ponit 3. 83 =g -4 î+ (9-27 - 7 832=83-82=+3î+(y-4)] t2 À Now Ezi= 81 ( _4ĉ Hy-2)7- +47)34649+42727272 E32-82 (3ůrg-A)ī +22 4 Trey 3924G+4)24217213)2 ++43 +42 Now Ezz - Egia 20 field to be o at yi- 540 (3ĉ+(4+57 +2k) – 2256-4€+4-239-7€) (13 +(3-432) 312 (65+(y-2) 2) 3/2 Now equation Consecutive termo- 540 X 3 -225x4 (13 + Y-4) 2) 319 (65+Y 28) 3/2 equal And these can never be apne term is positive and other in negative con never equate so no y posible on yaxio. -