Introduction:
When a charged particle moves in a magnetic field, it experiences a force called the Lorentz force. This force can cause the particle to deviate from its original path. In order for the particle to go undeflected, an electric field can be applied in a specific direction and magnitude to counteract the magnetic force.

Key Concepts:
1. Lorentz force: The force experienced by a charged particle moving in a magnetic field is given by the equation F = q(v × B), where F is the force, q is the charge of the particle, v is its velocity, and B is the magnetic field.
2. Electric field: The force experienced by a charged particle in an electric field is given by the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field.

Analysis:
In this scenario, the charged particle is moving parallel to a long straight conductor carrying current I in the positive X-axis direction. To find the direction and magnitude of the electric field required for the particle to go undeflected, we need to determine the magnetic force acting on the particle and then apply an electric field to counteract this force.

The magnetic field produced by the current-carrying conductor can be determined using Ampere's Law. Since the conductor is straight and the current is flowing in the positive X-axis direction, the magnetic field will circulate around the conductor in a clockwise direction when viewed from above.

Steps:
1. Determine the direction of the magnetic field using the right-hand rule for a current-carrying conductor.
2. Use the Lorentz force equation F = q(v × B) to calculate the magnetic force acting on the particle.
3. Apply an electric field in the opposite direction to the Lorentz force to counteract it.
4. Calculate the magnitude of the electric field using the equation F = qE.

Conclusion:
By applying an electric field in the opposite direction to the Lorentz force acting on the charged particle, we can ensure that the particle goes undeflected. The magnitude of the electric field can be determined by equating the force due to the electric field to the Lorentz force. It is important to note that the direction and magnitude of the electric field may vary depending on the specific values of the charge, mass, velocity, and current in the system.