Charge in a Magnetic Field question

[Lonewolf393]

Homework Statement

These are two similar questions, one from my previous exam and one from a sample test my teacher provided. I understand how to work the problem, but my question is how is the i or j component decided in each of these?

Homework Equations

From our formula sheet...

The Attempt at a Solution

 

[kuruman]

There is a coordinate system provided that gives the direction of the unit vectors. The direction of the force on charge q (assuming it is positive) is the same as the direction of the induced current at the position of the charge if the dotted circle were a circular metal loop. The induced current can either be clockwise or counterclockwise. This eliminates all the $\hat{j}$ options in the first picture and all the $\hat{i}$ options in the second picture. The sign depends on whether you have clockwise or counterclockwise current flow. Can you figure that out?