Magnetic Field of Solenoids – Rankers Physics

Magnetic Field Due to Circular Current Carrying Wire: Practice Problem & Solution

Consider two long solenoids \( A \) and \( B \) having length \( 2L \) and \( 3L \) and number of loop as \( N \) and \( 2N \) respectively. If both have same current then ratio of magnetic field inside \( A \) to that of the \( B \) will be
\( \frac{3}{4} \)
\( \frac{3}{2} \)
\( 1 \)
\( \frac{1}{2} \)

Solution Explained:

To solve this problem, we apply the core principles of Magnetic Field Due to Circular Current Carrying Wire. Understanding the underlying formula is key to arriving at the correct answer below:

The magnetic field inside a solenoid is given by \( B = \mu_0 \frac{N}{L} I \). Calculating the ratio: \( \frac{B_A}{B_B} = \frac{N_A / L_A}{N_B / L_B} = \frac{N / 2L}{2N / 3L} = \frac{3}{4} \).

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