Question

Strength of magnetic field produced by a current carrying solenoid depends upon :

• A. Number of turns
• B. Current
• C. Nature of core
• D. All the above

Hint:

The magnetic field of a solenoid is described by $B = \mu n I$. This formula directly shows that the strength of the magnetic field is dependent on the permeability of the core material ($\mu$), the number of turns per unit length ($n$), and the current ($I$).

Answer 1

The Correct Option is D

Step 1: Understand what a solenoid is and how it produces a magnetic field.
A solenoid is a long coil containing a large number of close turns of insulated copper wire. When an electric current flows through a solenoid, it produces a magnetic field similar to that of a bar magnet. The magnetic field lines inside a long straight solenoid are nearly uniform and parallel to the axis of the solenoid. Step 2: Recall the factors affecting the strength of the magnetic field of a solenoid.
The strength of the magnetic field ($B$) inside a solenoid is given by the formula:
$B = \mu n I$
where:
$B$ is the magnetic field strength.
$\mu$ is the magnetic permeability of the core material inside the solenoid.
$n$ is the number of turns per unit length of the solenoid (i.e., $n = N/L$, where $N$ is the total number of turns and $L$ is the length of the solenoid).
$I$ is the current flowing through the solenoid.
Let's analyze each factor mentioned in the options: Factor 1: Number of turns (specifically, number of turns per unit length)
From the formula $B = \mu n I$, it is clear that $B$ is directly proportional to $n$ (number of turns per unit length). A higher number of turns (for a given length) means a stronger magnetic field. So, 'Number of turns' (implicitly, number of turns per unit length) affects the strength. Factor 2: Current
From the formula $B = \mu n I$, it is clear that $B$ is directly proportional to $I$ (current). A larger current produces a stronger magnetic field. So, 'Current' affects the strength. Factor 3: Nature of core
The term $\mu$ in the formula represents the magnetic permeability of the core material inserted inside the solenoid.
For a solenoid with an air core or vacuum, $\mu = \mu_0$ (permeability of free space).
If a soft iron core (a ferromagnetic material) is placed inside the solenoid, the magnetic permeability ($\mu$) of the core material is much greater than $\mu_0$. This significantly increases the strength of the magnetic field produced. So, the 'Nature of core' affects the strength. Step 3: Conclude based on the analysis.
Since the strength of the magnetic field produced by a current-carrying solenoid depends on the number of turns (per unit length), the current flowing through it, and the nature of the core material, all the listed factors influence the magnetic field strength. Step 4: Compare with the given options.
Option (4) "All the above" correctly summarizes that the strength depends on all three factors. (4) All the above