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 determine the magnetic field \( B \) inside a solenoid, we use the following formula: \[ B = \mu_0 n I, \] where: \( \mu_0 \) is the permeability of free space (\( \mu_0 = 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A} \)), \( n \) is the number of turns per unit length, \( I \) is the current flowing through the solenoid. Step 1: Understanding \( n \) (Turns per Unit Length) The number of turns per unit length \( n \) is defined as: \[ n = \frac{N}{L}, \] where: \( N \) is the total number of turns in the solenoid, \( L \) is the length of the solenoid. Step 2: Substituting \( n \) into the Magnetic Field Formula By substituting \( n = \frac{N}{L} \) into the magnetic field formula, we get: \[ B = \mu_0 \left( \frac{N}{L} \right) I = \frac{\mu_0 N I}{L}. \] Conclusion: The magnetic field inside a solenoid is directly proportional to the current \( I \) and the number of turns per unit length \( n \). Therefore, the correct expression for the magnetic field \( B \) is: \[ B = \mu_0 n I. \] Final Answer: \[ \boxed{ \mu_0 n I } \]