Question

What is the magnetic field produced inside a solenoid?

• A. \( \frac{nN}{L} \)
• B. \( \frac{B}{\mu_0} \)
• C. \( \mu_0 n I \)
• D. \( \frac{n}{L} \)

Hint:

A solenoid generates a uniform magnetic field inside it, and the field strength depends on the current and the number of coils per unit length.

Answer 1

The Correct Option is C

To calculate the magnetic field \( B \) within a solenoid, the formula employed is:\[B = \mu_0 n I,\]with the following definitions: \( \mu_0 \) represents the permeability of free space, quantified as \( \mu_0 = 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A} \). \( n \) denotes the count of turns per unit length. \( I \) signifies the current flowing through the solenoid.Step 1: Defining \( n \) (Turns per Unit Length)The term \( n \), the number of turns per unit length, is mathematically defined as:\[n = \frac{N}{L},\]where: \( N \) is the total number of turns comprising the solenoid. \( L \) is the physical length of the solenoid.Step 2: Integration of \( n \) into the Magnetic Field EquationBy substituting the expression for \( n \) into the primary magnetic field formula, we obtain:\[B = \mu_0 \left( \frac{N}{L} \right) I = \frac{\mu_0 N I}{L}.\]Summary:The magnetic field intensity inside a solenoid exhibits a direct proportionality to both the current \( I \) and the number of turns per unit length \( n \). Consequently, the definitive expression for the magnetic field \( B \) is:\[B = \mu_0 n I.\] Final Result:\[\boxed{ \mu_0 n I }\]