Chapter 26, Problem 1FTD

An electron moving with velocity $\stackrel{\to }{v}$ through a magnetic field $\stackrel{\to }{B}$ experiences a magnetic force $\stackrel{\to }{F}$. Which of the vectors $\stackrel{\to }{F},\stackrel{\to }{v}$, and $\stackrel{\to }{B}$ must be at right angles?

To determine

Which of the vectors are at right angles to each other.

Answer to Problem 1FTD

Vectors $\overrightarrow{F},\overrightarrow{v}\text{and}\overrightarrow{B}$ are perpendicular to each other.

Explanation of Solution

Write the equation to find the force acting on a particle in magnetic field.

$F=qv\times B$

Here,

$F$ is the force

$q$ is the charge

$v$ is the velocity

$B$ is the magnetic field

From the equation we can see that both velocity vector and magnetic field vector are perpendicular to each other and they are both perpendicular to the force.

Therefore all the three vectors are perpendicular to each other.

Conclusion:

Therefore, vectors $\overrightarrow{F},\overrightarrow{v}\text{and}\overrightarrow{B}$ are perpendicular to each other.