A long solenoid of radius $1 ext{ mm}$ has $100$ turns per mm. If $1 ext{ A}$ current flows in the solenoi

Question

A long solenoid of radius $1 	ext{ mm}$ has $100$ turns per mm. If $1 	ext{ A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

Accepted Answer

1.  **Identify Formula:** The magnetic field ($B$) inside a long solenoid is given by $B = \mu_0 n I$, where $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$, $n$ is the number of turns per unit length, and $I$ is the current.
2.  **Unit Conversion:** The number of turns density is given in turns per mm. Convert this to SI units (turns per meter).
    $$n = 100 	ext{ turns/mm} = 100 	imes 10^3 	ext{ turns/m} = 10^5 	ext{ turns/m}$$
3.  **Substitute Values:**
    *   $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$
    *   $n = 10^5 	ext{ m}^{-1}$
    *   $I = 1 	ext{ A}$
    $$B = (4\pi 	imes 10^{-7}) 	imes (10^5) 	imes 1$$
4.  **Calculate:**
    $$B = 4\pi 	imes 10^{-2} 	ext{ T}$$
    $$B \approx 4 	imes 3.14 	imes 10^{-2} 	ext{ T}$$
    $$B = 12.56 	imes 10^{-2} 	ext{ T}$$

Step-by-Step Solution

Practice All PHYSICS Questions