Example

Question:

If the magnetic field is parallel to the positive \(y\)-axis and the charged particle is moving along the positive \(x\)-axis (Fig. 4.4), which way would the Lorentz force be for (a) an electron (negative charge), (b) a proton (positive charge)?

Solution:

The velocity \(\mathbf{v}\) of particle is along the \(x\)-axis, while \(\mathbf{B}\), the magnetic field is along the \(y\)-axis, so \(\mathbf{v} \times \mathbf{B}\) is along the \(z\)-axis (screw rule or right-hand thumb rule).
So, (a) for electron it will be along \(-z\) axis.
(b) for a positive charge (proton) the force is along \(+z\) axis.