Current flowing through a long solenoid is varied. Then, magnetic flux density of the magnetic field inside it varies :

Options

A. inversely with I
B. inversely with`I^(2)`
C. directly with I
D. directly with `I^(2)`

Explanation

To solve the question regarding how the magnetic flux density inside a long solenoid varies with the current flowing through it, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of a Solenoid**:
A solenoid is a long coil of wire that produces a magnetic field when an electric current passes through it. The magnetic field inside a long solenoid is uniform and can be calculated using a specific formula.

2. **Magnetic Flux Density Formula**:
The magnetic flux density (B) inside a long solenoid is given by the formula:
\[ B = \mu n I \]
where:
- \( B \) is the magnetic flux density,
- \( \mu \) is the permeability of the material inside the solenoid,
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current flowing through the solenoid.

3. **Analyzing the Formula**:
From the formula \( B = \mu n I \), we can observe that:
- \( \mu \) (permeability) and \( n \) (number of turns per unit length) are constants for a given solenoid.
- The only variable that affects \( B \) is the current \( I \).

4. **Direct Proportionality**:
Since \( B \) is directly proportional to \( I \), we can conclude that:
\[ B \propto I \]
This means that if the current \( I \) increases, the magnetic flux density \( B \) also increases, and vice versa.

5. **Conclusion**:
Therefore, the magnetic flux density of the magnetic field inside the solenoid varies directly with the current flowing through it.

### Final Answer:
The magnetic flux density of the magnetic field inside the solenoid varies directly with the current \( I \).

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