False

Explanation:
Inside a conductor, the magnetic field intensity is not zero. It is only zero in certain specific regions of a conductor.

1. Magnetic Field Inside a Conductor:
When a current flows through a conductor, a magnetic field is generated around it. According to Ampere's law, the magnetic field intensity (B) is directly proportional to the current (I) flowing through the conductor. Therefore, there is indeed a magnetic field inside a conductor.

2. Distribution of Magnetic Field:
The magnetic field inside a conductor is not uniform. It is concentrated near the surface of the conductor and decreases as we move towards the center. This non-uniform distribution is due to the skin effect, which causes the current to flow more on the surface of a conductor.

3. Magnetic Field Lines:
The magnetic field lines inside a conductor form closed loops. They travel parallel to the surface and do not intersect with each other. This is because the magnetic field lines always form closed loops and do not have any starting or ending point.

4. Magnetic Field Inside a Hollow Conductor:
If there is a hollow conductor, the magnetic field inside it is zero. This is because the current in a conductor flows on the surface, and in the case of a hollow conductor, there is no current flowing through the interior.

5. Magnetic Field Inside a Solid Conductor:
In the case of a solid conductor, the magnetic field inside is not zero. As mentioned earlier, the magnetic field is concentrated near the surface and decreases towards the center. Therefore, there is a non-zero magnetic field inside a solid conductor.

In conclusion, the statement that the magnetic field intensity is zero inside a conductor is false. The magnetic field inside a conductor is not zero, but it is non-uniform and concentrated near the surface.