Question

We have a solenoid made of stainless steel with 50 turns/m. The diameter of the wire is 2mm and when stretched it is 10m. What is the value of the magnetic field inside, in the center, when we apply a 5v DC voltage at its ends?

Answer 1

Answer:

The value of the magnetic field inside in the center is $0.89759\times10^{-3}\ T$.

Explanation:

Given that,

Number of turns per length = 50

Diameter = 2 mm

Stretched = 10 m

Voltage = 5 V

We need to calculate the resistance

Using formula of

$R=\dfrac{\rho l}{A}$

$R=\dfrac{4\rho l}{\pi d^2}$

Put the value into the formula

$R=\dfrac{4\times1.1\times10^{-7}\times10}{\pi\times(2\times10^{-3})^2}$

$R=0.35\ \Omega$

We need to calculate the magnetic field

Using formula of magnetic field

$B = \mu_{0}nI$

$B=\mu_{0}n\times\dfrac{V}{R}$

$B=4\pi\times10^{-7}\times50\times\dfrac{5}{0.35}$

$B=0.89759\times10^{-3}\ T$

Hence, The value of the magnetic field inside in the center is $0.89759\times10^{-3}\ T$.