Question

Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.6000 T vertically downward. The electric field is 2.000 x 106 V/m horizontally east. An electron, traveling horizontally northward, experiences zero resultant force from these fields and so continues in a straight line. What is the electron's speed? m/s

Answer 1

$\text{Solution :}\\ \text{Lorentz force on a charge moving in the region of electric and magnetic field is given by;}\\ \vec F=q (\vec E+\vec v \times \vec B) \ \\ \text{given that net force on the electron is zero. F= 0}\\ Then;\\ \vec E=-\vec v \times \vec B\\ and \ \\ \vec v\perp \vec B \\ Then\\ E = v \ B\\ \ \\ v = \dfrac{E}{B}\\ \ \\ v =\dfrac{2.000\times10^6 \ V/m}{0.6000\ T}\\ or\\ \text {Speed of the electron } \ \ v = 3.33\times 10^6m/s$