Lorentz force on an electron

Problem

An electron ($|q| = 1{,}6\cdot 10^{-19}$ C) enters perpendicularly into a magnetic field of magnitude $B = 0{,}5$ T with velocity $v = 2{,}0\cdot 10^5$ m/s. Calculate the magnitude of the Lorentz force.

Solution

Since the velocity is perpendicular to the field ($\vec v\perp\vec B$), the angle between the two vectors is $90^\circ$ and $\sin\theta = 1$. The magnitude of the Lorentz force is therefore $F = |q|\,v\,B\,\sin\theta = |q|\,v\,B$ Substituting the numerical values: $F = 1{,}6\cdot 10^{-19}\cdot 2{,}0\cdot 10^5\cdot 0{,}5$ $\ev{F \approx 1{,}6\cdot 10^{-14}\;\text{N}}$

Links

Topics: Magnetismo Concepts: Forza di Lorentz