Question

A wire is wound on a long rod of material of relative permeability ${\mu }_r=4000$ to make a solenoid. If the current through the wire is $5A$ and number of turns per length is $1000$ per meter, then the magnetic field inside the solenoid is:

• A. $25.12mT$
• B. $12.56mT$
• C. $12.56T$
• D. $25.12T$

Answer 1

The correct option is D $25.12T$

Given that,

Relative permeability, ${\mu }_r=4000$

Carried current, $I=5A$

Number of turns, $n=1000$

Therefore,

The magnetic intensity,

$H=nI$

$H=1000\times 5$

$H=5000A{m}^{-1}$

Now, the magnetic field inside the solenoid is

$B=\mu H$…. (I)

We know that,

$\mu ={\mu }_0{\mu }_r$

$\mu =4\pi \times {10}^{-7}\times 4000$

Now put the value of $\mu$ in equation (I)

$B=\mu H$

$B=4\pi \times {10}^{-7}\times 4000\times 5000$

$B=2\times 4\pi$

$B=8\times 3.14$

$B=25.12T$

Hence the magnetic field inside the solenoid is $B=25.12T$.