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 unit length is $1000$ per metre, then the magnetic field inside the solenoid is:

• A. $25.12mT$
• B. $12.56mT$
• C. $25.56T$
• 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,
$H=nI$
$H=1000\times 5=5000A{m}^{-1}$
Now, the magnetic field inside the solenoid is
$B=\mu H$.....(i)
We know that,
$\mu ={\mu }_0{\mu }_r=4\pi \times {10}^{-7}\times 4000$

We get,
$B=4\pi \times {10}^{-7}\times 4000\times 5000$
$B=25.12T$