Rankers Physics

Ampere's Circuital Law: Practice Problem & Solution

A long solenoid of $50text{ cm}$ length having $100$ turns carries a current of $2.5text{ A}$. The magnetic field at the centre of the solenoid is:  ($\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}$) (2020)
$3.14 \times 10^{-4}\text{ T}$
$6.28 \times 10^{-5}\text{ T}$
$3.14 \times 10^{-5}\text{ T}$
$6.28 \times 10^{-4}\text{ T}$

Solution Explained:

To solve this problem, we apply the core principles of Ampere's Circuital Law. Understanding the underlying formula is key to arriving at the correct answer below:

The number of turns per unit length is $n = \frac{N}{L} = \frac{100}{0.5\text{ m}} = 200\text{ turns/m}$. Using the formula $B = \mu_0 n I$, we substitute $\mu_0 = 4\pi \times 10^{-7}$, $n = 200$, and $I = 2.5\text{ A}$ to get $B = 6.28 \times 10^{-4}\text{ T}$.

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