Question

The $B-H$ curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with $1000 turns/cm$. The current that should be passed in the solenoid to demagnetize a ferromagnet completely is:

a) $2mA$
b) $1mA$
c) $3mA$
d) None of these

Answer 1

Hint: B-H curve shows that a given material doesn’t not follow the same path during magnetization and demagnetization. This creates a difference in the current, which is responsible for reduction of magnetization of the material. The current, at which the current demagnetizes, no longer remains zero but has a negative value. We will use this concept along with the basic formula to find the answer.

Formula used: $Hl=NI$

Complete step by step answer:
The B-H curve represents the magnetization and demagnetization characteristics of a ferromagnetic material. It shows the amount of current required for a particular magnetization to be achieved. It also shows that for a given ferromagnetic material, the path traced during magnetization and demagnetization are not the same.
We know that the magnetic intensity has a unique relation with the current passing through the conducting wire along with the number turns. This relation is as follows:
$Hl=NI$
Where, $H$ is the magnetic field intensity, $l$ is the length of conductor, $N$ is the number of turns, $I$ is the current through the conductor.
We can modify the above equation as:
$H=\dfrac{N}{l}I$ ------(i)
Here, it can be clearly seen that for the complete demagnetization of the ferromagnetic material, the y-axis component must be zero, i.e., $B=0$. Clearly, at this point the value of $H$ is $100A/m$.
Putting this value of $H$ in equation (i), we get:

$\dfrac{100A}{m}=\dfrac{1000turns}{{{10}^{-2}}m}I$
$I=1mA$

So, the correct answer is “Option B”.

Note: Don’t panic when length is not mentioned in such questions. Generally, the length is already present in other parameters often disguised. For example, here length was present in the $N$ given in question as $turns/m$. Hence, because of this, we did not require the absolute length to solve the question.