Consider a point charge q moving arbitrar ily along a trajectory described by vector function of time r (t). The velocity of the charge is thus V(t)- di,(t)/dt. Suppose Q and Q'represent points o...
Consider a point charge q moving arbitrar ily along a trajectory described by vector function of time r (t). The velocity of the charge is thus V(t)- di,(t)/dt. Suppose Q and Q'represent points on the trajectory where the charge is at time t and was at an earlier time t'. Let R(t) F r,(t) be the vector from the charge to the fixed point P as shown in the figure of particle re volume element de r" a) Prove the...
8. The position vector r of a point P is a function of the time t and r satisfies the vector differential equation d2r dr 2k (k2 n2)r g, dr2 where k and n are constants and g is a constant vector. Solve dr a and dt this differential equation given that r v when t = 0, a and v being constant vectors Show that P moves in a plane and write down the vector equation of this plane...
4. Uniformly moving point charge A point charge q is in uniform motion with velocity v = vzˆ, where v is a constant. At time t = 0 the charge is located at the origin. At a later time t 0 , at the field point x = x0, y = z = 0: (a) Find the scalar and vector potential. (b) What coordinate components does the electric field have? (c) What coordinate components does the magnetic field have? (d)...