Let's go through the task:

You provided three sub-questions with diagrams in the image:

1. Sub-question (a) asks to determine the direction of the force acting on a conductor carrying current in a magnetic field (illustrated in fig. 105, a).
2. Sub-question (b) asks to determine the direction of the current in the conductor (illustrated in fig. 105, b).
3. Sub-question (c) asks to determine the direction of the magnetic field lines of induction (illustrated in fig. 105, c).

Now let's analyze these sub-questions based on the right-hand rule:

(a) Direction of Force in a Magnetic Field

• In fig. 105 (a), a conductor is placed in a magnetic field created by a magnet (with north "N" and south "S" poles).
• According to the right-hand rule for the motor effect (Lorentz force), when the thumb points in the direction of the current and the fingers point in the direction of the magnetic field (from north to south), the palm pushes in the direction of the force.
• Here, the current $I$ flows to the right, and the magnetic field lines go from "N" to "S" (downward). Thus, the force $F$ acts outward from the page.

(b) Direction of Current in the Conductor

• In fig. 105 (b), the magnetic field is directed into the page (represented by "x" symbols), and the force $F$ is directed to the right.
• Using the right-hand rule again, with the fingers pointing into the page (magnetic field) and the palm facing the direction of the force (right), the thumb should point in the direction of the current. This means the current $I$ flows upward.

(c) Direction of Magnetic Field Induction

• In fig. 105 (c), the current is directed into the page (represented by the circle with a cross), and the force $F$ is to the right.
• Using the right-hand rule, with the thumb pointing into the page (current) and the palm facing the direction of the force (right), the fingers will curl in the direction of the magnetic field. Thus, the magnetic field lines go upward from the bottom of the image.

Would you like a detailed explanation of any part?

Here are five related questions to deepen your understanding:

1. What is the Lorentz force, and how does it apply to conductors in a magnetic field?
2. How does the right-hand rule differ for motors and generators?
3. Why do the magnetic field lines always flow from the north pole to the south pole of a magnet?
4. What happens to the force on the conductor if the current is reversed?
5. How do you determine the strength of the force on a conductor in a magnetic field?

Tip: Always remember that the right-hand rule is used for conventional current (positive to negative flow). If you deal with electron flow (negative to positive), the directions are reversed.