Question

Hello, I need help with a problem for my Electromagnetism II class. Please explain what to do and how to do it. I need help understanding it so I can do other problems like this.

Answer 1

Let Position of particle at time t will be by the V (4x + ( (4) +1) so °°41+1, 3141 (o, . ☺ = És A Be Bolle (0, y, z Now from Newton's Law F = m ă or F = 9l + T x B Now ïx b= l į - į? 1 | j ¿ 1 B. 00 - Bżŷ - By @ put in o q( Eg ² t Bzů By § 1 = mlý ý t ² ² ] or separating ŷ and i components q Bo ż = m Ý and q E-a B ý = më e Now, Let w=9B , so ed @ becomes ů = w ż and Ž = w/ Es ujj so these two are differential equation (Homogenous) Solutions and - ylt) = A Cus wt t B sinut t Ettc and alt) = B Coswt - A sinwit & no Now given initial condition - 4 (0)=0 and Zlog to gives 0 ALtc A +C =0 majand os 6+D-6)

4 col = -WA sin wt + B'w cos wt + E + C = 0 j(o)= 0 + BW + E +0=0 Bws + to co — = 6W= B's - Ed and i lol = -B'sinwt. w owA coswt = -WA= o 3 Aeol Put in So Le-o] also put in G B'= -0 or D = B. put in @ we get a (y(t) = -Es sinwk + E + - and 2(t) = - cos wat + 5 Now žloleo so 24) = Eo –® ] W Bo er o s o are required eigh of motion.