) An electron moving along the x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, what is the direction of the magnetic field in this region

- z direction

Explanation:

To find the direction of the magnetic field, you take into account that the magnetic force over a charge, is given by the following cross product:

     (1)

F_B: magnetic force

q: charge of the particle

v: velocity of the charge

B: magnetic field

In this case you have that the electron is moving along x-axis. You can consider this direction as the ^i direction. The electron experiences a magnetic deflection in the -y direction, that is, in the -^j  direction.

By the cross products between unit vectors, you have that:

-^j = ^i X ^k

That is, the cross product between two vectors, one in the +x direction, and another one in the +z direction, generates a vector in the -y direction. However, it is necessary to take into account that the negative charge of the electron change the sign of the result of the cross product, which demands that the second vector is in the -z direction. That is:

-^i X -k^ = ^i X ^k = - ^j

Hence, the direction of the magnetic field is in the -z direction

i guess it’s a and b

a. are