Question

5. The single charge 91 = 3 uC is located in the space at cartesian coordinates P1 = [0,0,3]. 91 is under the influence of both a point charge Q = 3 uC at location P2 = [0,0,0] and a magnetic field of B = [0,0,0.5] T at pį. The velocity of q, at location p, is represented by the velocity vector ✓ = [0,106,0] m/s. Find the sum of all forces (electrical and magnetic) acting on 91 in its current location and express your answer in vector form. (8 marks total)

Answer 1

© E q velocity 1 Electric Force & (JxB) B - Magnetic field Magnetic force due to point charge a. Electric Field Р At point p, Electric field due to a 9x109 Nmct an to 1 4п €о 2 Electric force at on charge Bar F anto Z (0,0,5) + . - 3 uc 3m 1 repulsion (as both (0,0,0) -Buc tve charge) X So Electric Force 1 Qui Х Fe THEO 72 3x10-6 x 3x10-6 98109 X N. 32 9x10-3 N.

V B = [0,0,0.5] T 0.5 ĥ [o 10601 m/s 106 ŷ m/s Ta A k ŷ x ^ = ûxi = Magnetic Force Fm Na (W x B) 3x10-6 ( 6 10 6 9 x 0.5 k) N 3x10-6 x 1068 0.5.1 11 N 1.5 i N Sum of total forces acting on vi = F = Fet Fm (9x10-3 û + 1057) N - 1:51 +9610-3 N (AN) F= [ 1.5 o 9810-31 N