Question

In an experiment to measure the velocity of electrons, an electric field $\left(E\right)$ and a magnetic field $\left(B\right)$ are employed to produce zero deflection. Then :

• A. The two fields are parallel and the velocity is given by $BE$
• B. The two fields are perpendicular and the velocity is given by $E/B$
• C. The two fields are parallel and the velocity is given by $E/B$
• D. The two fields are perpendicular and the velocity is given by $BE$

Answer 1

The correct option is B The two fields are perpendicular and the velocity is given by $E/B$

The electric force on electron of charge $e$ is,

$F=eE$

where, E = electric field.

And Magnetic force ,

$F=e$ $(V\times B)$

where, V= velocity of electron in magnetic field

B= magnetic field

From the above equations,

$E=V\times B$

Electric field E is perpendicular to both velocity of electron and the magnetic field. So, The two field is perpendicular to each other and the velocity of electron is $\frac{E}{B}$.

B. The two fields are perpendicular and the velocity is given by $\frac{E}{B}$.