Question

The electrons in the beam of a television tube have an energy of 19.0 keV. The tube is oriented so that the electrons move horizontally from north to south. At the electron's latitude the vertical component of the Earth's magnetic field points down with a magnitude of 42.3 μT. What is the direction of the force on the electrons due to this component of the magnetic field?

Answer 1

The direction is due south

Step-by-step explanation:

From the question we are told that

The energy of the electron is
`E = 19.0keV = 19.0 *10^3 eV`

The earths magnetic field is
`B = 42.3 \muT = 42.3 *10^(-6) T`

Generally the force on the electron is perpendicular to the velocity of the elecrton and the magnetic field and this is mathematically reresented as

`\= F = q (\= v * \=B)`

On the first uploaded image is an illustration of the movement of the electron

Looking at the diagram we can see that in terms of direction the magnetic force is

`\= F =q(\=v * \= B)= -( -\r i * - \r k)`

`= -(- (\r i * \r k))`

generally i cross k = -j

so the equation above becomes

`\= F = -(-(- \r j))`

`= - \r j`

This show that the direction is towards the south