To calculate the magnetic susceptibility, we first need to understand the concepts of magnetic induction and magnetic susceptibility.

Magnetic Induction:
Magnetic induction, denoted by B, is the measure of the magnetic field strength in a given region. It represents the magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. The SI unit of magnetic induction is the Tesla (T).

Magnetic Susceptibility:
Magnetic susceptibility, denoted by χ, is a property of a material that describes its response to an applied magnetic field. It quantifies how easily the material can be magnetized. Magnetic susceptibility is dimensionless and can be positive or negative.

Given information:
- The solenoid has 1000 turns per unit length.
- A current of 2 A is passing through the solenoid.
- The measured magnetic induction is 4×3.14 T.

Calculating Magnetic Susceptibility:
To calculate the magnetic susceptibility, we can use the formula:

χ = B / (μ₀ * H)

where
- χ is the magnetic susceptibility,
- B is the magnetic induction,
- μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A),
- H is the magnetic field strength.

In this case, the solenoid can be considered as an ideal solenoid with no magnetic material inside. Therefore, the magnetic field strength inside the solenoid is given by:

H = n * I

where
- H is the magnetic field strength,
- n is the number of turns per unit length,
- I is the current passing through the solenoid.

Given that n = 1000 turns per unit length and I = 2 A, we can calculate the magnetic field strength:

H = 1000 * 2 = 2000 A/m

Substituting the values of B and H into the formula for magnetic susceptibility:

χ = (4 × 3.14 T) / (4π × 10⁻⁷ T·m/A * 2000 A/m)

Simplifying the expression:

χ = (4 × 3.14) / (2000 × 10⁻⁷)

χ = 2 × 10¹⁰

Therefore, the magnetic susceptibility of the solenoid is 2 × 10¹⁰.

Explanation:
The magnetic susceptibility is a measure of how easily a material can be magnetized. In this case, the solenoid is considered as an ideal solenoid with no magnetic material inside, so the magnetic susceptibility is independent of any material properties. It is solely determined by the number of turns per unit length and the current passing through the solenoid. By using the formula for magnetic susceptibility and substituting the given values, we can calculate the magnetic susceptibility as 2 × 10¹⁰. This means that the solenoid can be easily magnetized when subjected to an applied magnetic field.