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find the path of motion of a charged particle in parametric form. MATH HELP NEEDED!!!?
A charged particle enters a uniform magnetic field with velocity that is not perpendicular to the direction of the magnetic field. Find its path of motion in parametric form (with parameter t = time). Assume that the speed of the particle is much smaller that the speed of light. the forces acting on the particle by the magnetic field is F = qv x B, where v = v_x(i) + v_y(j) +v_k(k) is the velocity of the charge in m/s at any instant, q is the charge in Coulomb, and B is the magnetic field in Tesla.
1 Answer
- NickyLv 57 years ago
You have the velocity of the charged particle in separated coordinate form. You need to know the direction of the magnetic field also in separate coordinates. That is, V(t) = Vx(t) + Vy(t) + Vz(t), these being the components of the velocity along (x,y,z) directions so I suppose I should introduce the unit vectors (i,j,k) {more precisely, i = (1,0,0), j = (0,1,0), k = (0,0,1)} so that properly written-out,
V(t) = i.Vx(t) + j.Vy(t) + k.Vz(t)
You prepare likewise the separate coordinate form B = i.Bx + j.By + k.Bz
Whereupon, F = qV x B and you can write this out according to the xyz component form of the cross product, that I'm not going to clatter the keys with.
