a)Looking sideways, into the screen is west...
b) Convert KE from eV into joules.
c) acceleration is always perpendicular to the velocity; the electrons are undergoing uniform circular motion. The radius of the path R below can be found from the relationship between velocity and centripetal acceleration; i.e., ac = v2/R.
The magnetic force on the wire must be upward and have a magnitude equal to the gravitational force on the wire. Apply the right-hand rule to show that the current must be from left to right.
Construct a free body diagram as follows:
Note that directly opposing the frictional force with the magnetic force is not the optimal configuration. An upward component of the magnetic force can be used to lower the normal force and thus the frictional force.
Consider the equilibrium conditions, balance of forces in the horizontal and vertical directions.
This should lead to an expression for the magnetic field needed:
which should be optimized for theta by differentiating and setting equal to zero. After finding the optimum angle, then solve for the minimum B.
Consider an infinitesimal segment of the loop, length ds. Evaluate the force that it experiences in the field at that point. Consider the contribution from its conjugate on the opposite side of the loop and determine the resultant direction.