Question

An electron is moving northward at 25 ,/s in a 4.5 T magnetic field pointing southward.

What is the force (magnitude and direction).

Answer 1

The force on a charged particle due to a magnetic field is given by the formula

F=q(TXB)

where is the charge of the particle, $\overrightarrow{v}$ is the velocity vector, and $\overrightarrow{B}$ is the magnetic field vector.

Here, we know that the direction of the velocity is anti-parallel to the magnetic field, i.e they are oriented at $180^\circ$ to each other. You may already know that for vecotrs anti-parallel to each other, their cross product is zero. Here, we will use that result and prove the force on the electron is zero.

F=q(TXB)

From the definition of the cross product

F=g(TIB sinon)

where $\overrightarrow{n}$ is a vector perpendicular to both the other vectors.

We know that . Substituting this, we get

Ꮎ = 180

F=g(TIB sin 180)

We also know that

sin 180 = 0

Therefore, .

F =0

There is no force acting on the electron.