Answer:
The direction is due south
Explanation:
From the question we are told that
The energy of the electron is [tex]E = 19.0keV = 19.0 *10^3 eV[/tex]
The earths magnetic field is [tex]B = 42.3 \muT = 42.3 *10^{-6} T[/tex]
Generally the force on the electron is perpendicular to the velocity of the elecrton and the magnetic field and this is mathematically reresented as
[tex]\= F = q (\= v * \=B)[/tex]
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
[tex]\= F =q(\=v * \= B)= -( -\r i * - \r k)[/tex]
[tex]= -(- (\r i * \r k))[/tex]
generally i cross k = -j
so the equation above becomes
[tex]\= F = -(-(- \r j))[/tex]
[tex]= - \r j[/tex]
This show that the direction is towards the south
