Animated Solution for Physics - Magnetic Effects of Current: The figure gives experimentally measured $B$ versus $H$ variation in a ferromagnetic material. The retentivity, coercivity and saturation respectively of the material are

The hysteresis loop is one of the most fascinating concepts in magnetism. It is not just a simple graph; it is the memory of a ferromagnetic material! When we plot the induced magnetic field $B$ against the applied magnetizing field $H$, the material doesn't just follow a straight line. It traces out a beautiful loop that tells us exactly how the material behaves under varying magnetic fields.

In this problem, we are given an experimentally measured $B-H$ curve and asked to find three critical parameters: retentivity, coercivity, and saturation. Let's break them down one by one by simply reading the graph.

Imagine you have a piece of iron, and you place it inside a strong magnetic field. The iron gets magnetized. Now, you turn off the external field, meaning $H=0$. Does the iron lose all its magnetism? No! The magnetic domains inside the iron like to stay aligned. The amount of magnetic field $B$ that remains in the material when $H=0$ is called its retentivity.

Geometrically, retentivity is simply the y-intercept of the hysteresis loop. If we look at the given graph, the curve crosses the positive y-axis at exactly $B=1.0\text{ T}$. Therefore, the retentivity of this material is $1.0\text{ T}$.

Now, suppose we want to completely demagnetize our piece of iron. Since it has a residual magnetic field of $1.0\text{ T}$, we need to apply a reverse magnetic field to force the domains back into a random orientation. The magnitude of this reverse magnetizing field $H$ required to make the induced field $B=0$ is known as coercivity.

On the graph, coercivity corresponds to the x-intercept on the negative side. Looking closely, the curve crosses the x-axis at $H=-50\text{ A/m}$. Since coercivity is defined as a magnitude, we take the positive value. Thus, the coercivity is $50\text{ A/m}$.

Finally, let's talk about saturation. When we keep increasing the applied magnetic field $H$ in the positive direction, the induced magnetic field $B$ also increases. However, this doesn't go on forever. Eventually, all the magnetic domains inside the material become perfectly aligned with the external field. Once this happens, increasing $H$ further will not increase $B$ significantly. The curve flattens out.

This maximum, constant value of $B$ is called the saturation magnetization. Looking at the top right of our graph, the curve levels off at a maximum height of $B=1.5\text{ T}$. Hence, the saturation value is $1.5\text{ T}$.

By carefully reading the graph, we have extracted all three parameters: - Retentivity = $1.0\text{ T}$ - Coercivity = $50\text{ A/m}$ - Saturation = $1.5\text{ T}$

Comparing these values with the given options, we find that they perfectly match option (a). This problem is a great reminder that sometimes, physics is just about knowing your definitions and knowing where to look on a graph!