Final answer:
Using the right-hand rule for negatively charged particles and considering the deflection of electrons towards the east, the magnetic field would technically be directed upwards. However, with only cardinal direction options given, the most appropriate answer is north, assuming the perspective is based on Earth's surface and how its magnetic field lines run from south to north.
Step-by-step explanation:
If electrons are flowing towards the south are deflected towards the east by a magnetic field, we can determine the direction of the magnetic field using the right-hand rule for negatively charged particles like electrons.
According to this rule, when you point your thumb in the direction of the electron's velocity (towards the south), and your middle finger in the direction of the force acting on it (towards the east), your index finger will point in the direction of the magnetic field acting on it.
Since electrons are negatively charged, we actually have to reverse the direction our palm would face (compared to positively charged particles), hence the direction of the magnetic field must point upwards.
Since the question specifies the deflection towards the east, we can use this deflection to establish that the force is acting perpendicular to the velocity of the electrons. As the Earth's magnetic field has vertical and horizontal components, in this scenario, we're considering the vertical component.
Therefore, the magnetic field direction cannot be east or west as these are in the horizontal plane. Given that the electrons are being deflected towards the east, the only possible direction in a vertical plane from the perspective of south-to-north direction of electron travel is upwards.
However, the question does not provide upwards as an option, and the standard choices are likely based on Earth's surface directions. Since the Earth's magnetic field lines emerge from the southern hemisphere and enter the northern hemisphere, and assuming the question expects an answer in relation to Earth's surface directions, the correct answer to the magnetic field's direction could be (a) North, despite the lack of conventional vertical options.