Please show all work! B11. When a charged particle moves with velocity v through a magnetic field B, a force due to the magnetic field FÅ actson the charged particle. This occurs according to the cross-product:FB= qv x Bwhere q is the charge of the particle.(a) If a particle of charge q=13.4 × 10−°C, where the unit C is a Coulomb, moves according to the velocityvector v = (1,5,2) and the magnetic field vector is B = (4, 2,−1), find the force vector FB that is acting onthe particle.(b) What is the magnitude of the force on the particle?(c) Sketch the right-handed system {v, B, FB} and roughly indicate the trajectory of the particle.

We will write the given vectors explicitly in cartesian vector form and substitute in the given…

11. When a charged particle moves with velocity v through a magnetic field B, a force due to the magnetic field FB acts on the charged particle. This occurs according to the cross-product: FB = qv x B where q is the charge of the particle. (a) If a particle of charge q = 13.4 x 10-6C, where the unit C is a Coulomb, moves according to the velocity vector v = (1,5, 2) and the magnetic field vector is B = (4, 2, -1), find the force vector FB that is acting on the particle. (b) What is the magnitude of the force on the particle? (c) Sketch the right-handed system {v, B, FB} and roughly indicate the trajectory of the particle.

11. When a charged particle moves with velocity v through a magnetic field B, a force due to the magnetic field FB acts on the charged particle. This occurs according to the cross-product: FB = qv x B where q is the charge of the particle. (a) If a particle of charge q = 13.4 x 10-6C, where the unit C is a Coulomb, moves according to the velocity vector v = (1,5, 2) and the magnetic field vector is B = (4, 2, -1), find the force vector FB that is acting on the particle. (b) What is the magnitude of the force on the particle? (c) Sketch the right-handed system {v, B, FB} and roughly indicate the trajectory of the particle.