In a current carrying long solenoid, the field produced does not depend upon

Options

A. Number of turns per unit length
B. Current flowing
C. Radius of the solenoid
D. All of these

Answer

To solve the question, we need to analyze the factors that influence the magnetic field produced by a long solenoid. The magnetic field inside a long solenoid is given by the formula:

\[ B = \mu_0 n I \]

where:
- \( B \) is the magnetic field inside the solenoid,
- \( \mu_0 \) is the permeability of free space (a constant),
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current flowing through the solenoid.

Now, let's break down the factors mentioned in the options:

1. **Number of turns (n)**: The magnetic field is directly proportional to the number of turns per unit length. Therefore, it does depend on this factor.

2. **Current (I)**: The magnetic field is also directly proportional to the current flowing through the solenoid. Thus, it depends on this factor as well.

3. **Length of the solenoid**: The formula for the magnetic field does not explicitly include the total length of the solenoid. However, the number of turns per unit length (n) can be affected by the length if the total number of turns is fixed. Therefore, it indirectly depends on the length.

4. **Radius of the solenoid**: The formula for the magnetic field does not include the radius of the solenoid. This means that the magnetic field inside a long solenoid is independent of its radius.

5. **All of this**: This option suggests that the magnetic field depends on all the factors mentioned, which is incorrect since we have established that the radius does not affect the magnetic field.

From this analysis, we can conclude that the magnetic field produced in a current-carrying long solenoid does not depend upon the radius of the solenoid.

### Final Answer:
The field produced in a current-carrying long solenoid does not depend upon the radius of the solenoid.