Question

A solenoid of 1000 turns per metre has a core of material with relative permeability 400. The windings of the solenoid are insulated from the core and a current of 2 A is passed through the solenoid. Then the value of the magnetic intensity inside the solenoid is

• A. $2\times10^3$ Am$^{-1}$
• B. 1.0 Am$^{-1}$
• C. $8\times10^5$ Am$^{-1}$
• D. 794 Am$^{-1}$

Hint:

Be careful to distinguish between magnetic field $B$ (in Tesla) and magnetic intensity $H$ (in A/m). For a solenoid, $H = nI$ is independent of the core, while $B = \mu H = \mu_r \mu_0 H$ depends on the core material. Read the question carefully to see which quantity is asked for.

Answer 1

The Correct Option is A

There are two related quantities inside a solenoid: magnetic field ($B$) and magnetic intensity ($H$).
Magnetic Field: $B = \mu n I$, where $\mu$ is the permeability of the core material.
Magnetic Intensity: $H = n I$.
The magnetic intensity $H$ depends only on the number of turns per unit length ($n$) and the current ($I$), and is independent of the core material.
We are given:
Number of turns per metre, $n = 1000$ turns/m.
Current, $I = 2$ A.
The relative permeability $\mu_r = 400$ is extra information, not needed for calculating $H$.
Now, we calculate the magnetic intensity $H$:
$H = n \times I = 1000 \text{ turns/m} \times 2 \text{ A}$.
$H = 2000$ A/m or Am$^{-1}$.
This can be written in scientific notation as $2 \times 10^3$ Am$^{-1}$.