The question asks to determine the direction of the magnetic force acting on a positively charged particle. The image displays three scenarios labeled 'a', 'б', and 'в', each showing a current-carrying wire and a charged particle with its velocity vector. Please determine the direction of the magnetic force for each scenario.

Analysis of the problem:

We need to determine the direction of the magnetic force on a positively charged particle moving in a magnetic field. The force is given by the Lorentz force equation: F = q(v × B). Since the charge q is positive, the force F is in the same direction as the cross product v × B.

The magnetic field B is generated by the current I in the wire. The direction of B can be found using the right-hand rule: point your thumb in the direction of the current I, and your fingers will curl in the direction of the magnetic field lines. The magnetic field lines form concentric circles around the wire.

Scenario a:

• The current I is directed to the right.
• The velocity v of the positively charged particle is directed to the right, parallel to the wire.
• Let's assume the particle is located above the wire. Applying the right-hand rule for the magnetic field (thumb to the right), the magnetic field B above the wire is directed out of the page.
• Now, we find the cross product v × B. v is to the right, and B is out of the page. Using the right-hand rule for cross products (fingers of the right hand point in the direction of v, curl towards the direction of B), the thumb points upwards.
• Therefore, for scenario 'a', the magnetic force on the particle is directed upwards.

Scenario б:

• The current I is directed to the right.
• The velocity v of the positively charged particle is directed to the right, parallel to the wire.
• This scenario is identical to scenario 'a' in terms of the direction of current and velocity relative to each other and the wire. Let's assume, as in 'a', that the particle is above the wire.
• The magnetic field B above the wire is directed out of the page.
• The cross product v × B (right × out of page) results in a force directed upwards.
• Therefore, for scenario 'б', the magnetic force on the particle is directed upwards.

Scenario в:

• The current I is directed to the right.
• The velocity v of the positively charged particle is directed upwards.
• Let's assume the particle is located above the wire. The magnetic field B above the wire is directed out of the page.
• Now, we find the cross product v × B. v is upwards, and B is out of the page. Using the right-hand rule for cross products (fingers of the right hand point in the direction of v, curl towards the direction of B), the thumb points to the left.
• Therefore, for scenario 'в', the magnetic force on the particle is directed to the left.

Summary of Force Directions:

• Scenario a: Upwards
• Scenario б: Upwards
• Scenario в: To the left