ACJC Applications of Vectors: Magnetic Force Assignment Q1

Applications of Vectors: Magnetic Force

A magnetic field exerts a force on a moving charge. Given a charge of \(q\) coulombs moving with velocity \(\mathbf{v}\), measured in ms\(^{-1}\), in a magnetic field \(\mathbf{B}\), measured in Teslas, the force, \(\mathbf{F}\) on the charge is given by

\(\mathbf{F}=q\left( \mathbf{v}\times \mathbf{B} \right)\), where \(\mathbf{F}\) is measured in Newtons.

A charge of \(1.6\times {{10}^{-19}}\) coulombs is moving with a speed of \(3\times {{10}^{6}}\) ms\(^{-1}\) in the direction of the vector \(2\mathbf{i}+2\mathbf{j}+\mathbf{k}\). The charge is moving in a region where the magnetic field is \(\mathbf{B}=4\mathbf{i}+2\mathbf{j}-3\mathbf{k}\). Find the force \(\mathbf{F}\) acting on the charge and the magnitude of this force.[4]