Question

The coercivity of a small bar magnet is $4 \times {10^3}A/m$. It is inserted inside a solenoid of 500 turns and length 1m to demagnetize it. The amount of current to be passed through the solenoid will be
(A) $2.5$A
(B) 5 A
(C) 8 A
(D) 10 A

Answer 1

Hint
When a bar magnet is placed inside a solenoid, it causes the bar magnet to demagnetize because of the magnetic field that forms inside the solenoid due to the current passing through it. So the intensity of the magnetic field has to be equal to the coercivity of the bar magnet. From there we can find the current passing through using the formula $H = nI$.
To solve this problem we will be using the following formula,
$\Rightarrow H = nI$
where $H$ is the intensity of the required magnetic field,
$n$ is the number of turns per unit length of the solenoid,
and $I$ is the current passing through the solenoid.

Complete step by step answer
The coercivity of any bar magnet means the intensity of the magnetic field that will be required to demagnetise it or reduce its magnetisation to zero. So the coercivity of a bar magnet is its resistance to becoming demagnetised.
Therefore the intensity of the magnetic field needed is given in the question as,
$\Rightarrow H = 4 \times {10^3}A/m$.
Now let us consider a current $I$ is passed through a solenoid of $n$ turns per unit length and it produces a magnetic intensity of $H$. So the formula is,
$\Rightarrow H = nI$
To find the current we arrange the equation as,
$\Rightarrow I = \dfrac{H}{n}$
Now in the question, it is given that we have a solenoid of 500 turns and a length of 1m. So to find the number of turns per unit length, we divide the number of turns by the length,
$\therefore n = \dfrac{{500}}{1}$
From here we have \[n = 500\] turns.
So we have can now put the values of $H$ and $n$ in the equation, and we get
$\Rightarrow I = \dfrac{{4 \times {{10}^3}}}{{500}}$
By doing the calculation we get,
$\Rightarrow I = 8A$
Therefore, a current of 8A is required to be passed through the solenoid.
So the correct answer is (C).

Note
The coercivity is the minimum value of the magnetic intensity that brings a magnetised substance back to its original state. In the case of a ferromagnetic substance, when the magnetic field is reversed in the direction the substance, after some time, loses its magnetisation completely.