Physics M.C.Q (1 Marks)

Superconductors are materials that conduct electricity with no resistance. This means that, unlike the more familiar conductors such as copper or steel, a superconductor can carry a current indefinitely without losing any energy.
The upper limit temperature of a superconductor is $125K$

The substances which are attracted towards a magnet are called ferro-magnetic materials Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic $($or ferrimagnetic$)$. These include iron, nickel, cobalt, some alloys of rare$-$earth metals, and some naturally occurring minerals such as lodestone.

Above $631K \ Ni$ behaves like paramagnetic material.

A magnetic dipole possess maximum potential energy when its magnetic moment and the magnetic field are antiparallel. When the magnetic dipole is aligned along the magnetic field, i.e. when $\theta = 180^\circ,$ it is in unstable equilibrium having maximum potential energy.

Diamagnetism $($where orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields$)$ is a property of all materials and opposes applied magnetic fields, but is very weak.

According to Lenz's law an induced electromotive force $(emf)$ always gives rise to a current whose magnetic field opposes the original change in magnetic flux.
It is a common way of understanding how electromagnetic circuits obey newton's third law and the conservation of energy.

The value of $H$ needed to remove the residual magnetism is coercive force or coercivity.

Key concept: The electrostatic field lines, do not form a continuous closed path (this follows from the conservative nature of electric field) while the magnetic field lines form the closed paths.
According to the Gauss' law, $\oint\text{E.ds}=\frac{\text{q}}{\in_0}$ for electronstatic field. It does not contradict foe eletrostatic fields as the elecric field lines do not form a continuous closed path.
According to Gauss' law in magnetism.
$\oint\text{B.ds}=0$
Which implies that number of magnetic field lines entering the Gaussian surface is equal to the number of magnetic field lines leaving it. Therefore case $(ii)$ is not possible.

Paramagnetic materials are those when suspended freely inside the magnetic field, it slowly sets itself parallel to the direction of the magnetic field. When placed in a non$-$uniform magnetic field, it tends to move from weaker to a stronger magnetic field.

Curie $-$ Wiess Law states that all ferromagnetic substances become paramagnteic above the curie temperature.

Points lying on the axis of a magnet are called end$-$on points. In our case, the point on the axis of the loop $($on replacing the circular loop with an equivalent magnetic dipole$)$ lies on the axis of the magnetic dipole or on the end$-$on position.
If P was the point on the axis of the loop, then it is clear from the figure that $P$ lies on the end$-$on position of the equivalent magnetic dipole.

Iron is a ferromagnetic substance the property which makes it attach to magnets. This causes the concavity. Chromium is anti$-$ferromagnetic, wood and carbon are not magnetic materials.

Magnetic lines of force start from the North Pole and end at the South Pole out side the bar magnet.
They are continuous through the body of magnet.
Magnetic lines of force are closed circular loops.
Two magnetic lines of force can not intersect each other because, if they intersect there will be two directions of magnetic field at the point of intersection, which is impossible.
Crowded magnetic lines of force show greater magnetic strength and vice$-$versa.

For a compass to show the direction of magnetic pole moment, they must be placed at ether of the $2$ geographic poles. It is because the direction of magnetic moment is from south to north pole.
The compass therefore will be vertical at both the poles.

The position of the points lying on the equator of a magnetic dipole is called the broadside$-$on position. In our case, the point on the loop $($after replacement of the circular loop with an equivalent magnetic dipole$)$ lies on the equatorial position of the equivalent magnetic dipole. Hence, the point lies on the broadside$-$on position.
If $P$ was the point on the loop, then it is clear from the figure that point $P$ lies on the broadside$-$on position of the equivalent magnetic dipole.

Permanent magnets are made up of materials having high retentivity, high coercivity, and high permeability such as steel. Other suitable materials for making permanent magnets are alnico $($an alloy of iron, aluminum, nickel, copper, and cobalt$),$ cobalt steel, and ticonal. That leaves zinc as the one that cannot be used to make permanent magnets.

The close continuous curves in a magnetic field are called magnetic lines of force. Curved lines are used to represent a magnetic field, drawn such that the number of lines relates to the magnetic field's strength at a given point and the tangent of any curve at a particular point is along the direction of magnetic force at that point.
The magnetic lines of force are uniform and strong at the point $C$ and they diverge as they move towards points $A$ and $B$ and the distance between the lines increases. Eventually, the strength of the magnetic field is strong where the lines are closer and they weaken as the closeness decreases.

The $SI$ unit of magnetic flux is Weber.

When suspended freely, a thin long piece of magnet comes to rest nearly in the geographical north$-$south direction. When placed in a non$-$uniform magnetic field, it tends to move from weaker to stronger magnetic field.

Oersted's law is the law that a steady electric current creates a magnetic field around it. This was discovered on April $21, 1820$, by Danish physicist Hans Christian Oersted $(1777–1851),$ when he noticed that the needle of a compass next to a wire carrying current turned.

Magnetic dipole moment $=$ Pole strength $\times $ Magnetic length.
Pole strength $=\frac{\text{Magnetic dipolemoment}}{\text{Magnetic length}}$
Pole strength $=\frac{5}{0.2}$
Pole strength $= 25 \ Am.$

When current is passed through a current carrying inductor, energy is stored in it in form of magnetic field.
Energy density is given by: $\text{n}_\text{B}=\frac{\text{B}^2}{2\mu}$

Magnetic field can penetrate through both magnetic and non$-$magnetic substances.

Diamagnetic material
$−1\leq \text{x}<0$
$0 \leq \mu < 1$
$χ =$ Magnetic susceptibility
$\mu =$ permeability

This problem is based on Magnetism.
Ferro$-$magnetism is the property of certain substances due to which they get strongly attracted to a magnet and strongly influenced in a magnetic field.
Certain substances like iron, nickel, cobalt, etc, are ferro$-$magnetic in nature.
Every atom of such materials, behave like small bar$-$magnets. The proper word is magnetic dipoles. In ferromagnetic materials, there are small regions known as domains. In each domain, all the atoms are alligned in one direction. All of them have their north$-$pole facing one side and their south$-$pole facing the other side. Hence every domain behaves like a dipole.
In the above picture, the arrows indicate the domains, pointing towards their north$-$poles.
In the absence of any magnetic field, all the domains are alligned randomly and so, the substance doesn't have any magnetic properties.
When the substance is placed in a weak magnetic field, a few domains turn and allign in the direction of the field, some domains which are already in the direction of the field expand slightly, and those alligned in direction opposite to the field, reduce in size. As a result, the entire substance has a mild dipole$-$like properties.
When the substance is placed in a strong magnetic field, many domains rapidly turn and allign in the direction of the field, the domains which are already in the direction of the field expand tremendously, and those alligned in direction opposite to the field, shrink so much that they almost disappear. As a result, all the domains are parallel to each other and alligned in one direction. The entire substance now becomes a strong bar$-$magnet.

Magnetic dip or inclination at a place is defined as the angle made by the Earth’s magnetic field with the horizontal in the magnetic
meridian. It is denoted by $\delta$.
Magnetic declination at a place is defined as the angle between the geographic meridian and magnetic meridian.

Space surrounding a magnet in which magnetic force is executed, is called a magnetic field.
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are most readily encountered with nearby permanent magnets, which pull on magnetic materials $($such as iron$)$ and attract or repel other magnets.

The magnetic field above the wire is out of the plane. This flux is decreasing and should be compensated by the current in the loop $F$ and so the current in loop $F$ will be anti$-$clockwise. For loop $G$ the situation is opposite

Angle of dip is $90^o$ at geographical North Pole because attraction on the North Pole of needle is very strong and the needle remains in vertical plane. At the magnetic equator, the needle will point horizontally, i.e. dip angle is $0^o$. As you move from the magnetic equator towards the magnetic pole, the angle increases in the northern hemisphere. So, the angle of dip is maximum.

When taken to a geomagnetic pole, a compass needle that is allowed to move in a horizontal plane will try to suspend itself vertically to the horizontal plane containing the compass. In other words, the horizontal plane containing the compass will restrict the compass to suspend itself in vertical direction; hence, the compass will stay in any position.
However, a freely suspended magnet will become vertical at poles, with its north pole pointing towards Earth at its north pole $($which is magnetic south$).$

Key concept: Toroid'. A toroid can be considered as a ring shaped closed solenoid. Hence it is like an endless cylindrical solenoid.


The magnetic field is only confined inside the body of a toroid in the form of concentric magnetic lines of force. For any point inside the empty space surrounded by toroid and outside the toroid, the magnetic field $B$ is zero because the net current enclosed in these spaces is zero. Thus, the magnetic moment of toroid is zero.
In general, if we take $r$ as a large distance outside the toroid, then $\text{m}\propto\frac{1}{\text{r}^3}$. But this case is not possible here.

When we break a magnet into two, both act as magnets, that is both have a north and south pole each. In both these pieces the corresponding north and south poles remain on the sides as in the original magnet. This means that the $2$ broken sides must get oppositely polarized.

Magnetic field $B$ due to a bar magnet of magnetic moment $M$ at distance r of the point on the axis from its centre is given by
$\text{B}=\frac{\mu_02\text{Mr}}{4\pi(\text{r}^2-\text{l}^2)^2}$
Here, $2l$ is the length of the magnet.
When the distance of the point where the magnetic field has to be calculated is greater than the length of the magnet, i.e $r >> l$, the bar magnet acts like a magnetic dipole whose magnetic field is
$\text{B}\propto\frac{1}{\text{r}^3}$
Now, $l$ in the denominator can be neglected.
So, the correct option is $(c).$

The magnetic dipole moment of a magnetic dipole is defined as the product of its pole strength and magnetic length. The $SI$ unit of magnetic dipole moment is ampere metre ${ }^2\left( Am ^2\right)$. Magnetic dipole moment is a vector quantity and is directed from south to north pole of the magnet.

A bar magnet does not exert a force or torque on itself due to its field. But an element of a current$-$carrying conductor experiences forces due to another element of the conductor. So, the torque exerted by a bar magnet on itself is zero.

The relative permeability of ferromagnetic materials is much larger than $1$. Ferromagnetic substances are those, which when placed in a magnetic field are strongly magnetized in the direction of the magnetizing field, i.e., it is strongly attracted by a magnet.

Ferromagnetic materials exhibit a long$-$range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain. Within the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetized because the many domains will themselves be randomly oriented with respect to one another. Ferromagnets will tend to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history" is called hysteresis.
\Nickel, iron and cobalt are such materials. Ferromagnetic materials exhibit a long$-$range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain. Within the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetized because the many domains will themselves be randomly oriented with respect to one another.Ferromagnets will tend to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history" is called hysteresis. Nickel, iron and cobalt are such materials.

Magnetic field $B$ due to a bar magnet of magnetic moment $M$ at distance $r$ of the point on the axis of the magnet from its centre is given by.
$\text{B}=\frac{\mu_\text{o}}{4\pi}\frac{2\text{Mr}}{(\text{r}^2-\text{l}^2)^2}$
Here, $2I$ is the length of the magnet.
So, from the above formula, it can be easily seen that $\text{B}\propto\frac{\text{r}}{(\text{r}^2-\text{r}^2)^2}$

Magnetic susceptibility of a magnetic substance is defined as the ratio of the intensity of magnetization $(I)$ to the magnetic intensity $(H).$ The expression is given by:
$\text{Xm}=\frac{\text{I}}{\text{H}}$
Magnetic susceptibility measures the aptness of a magnetic substance to acquire magnetism. It is a unit less constant of magnetic substance.

When we increase $H$ then $I$ also increases but when we decrease $HI$ does not becomes zero, and so as $B$ if we plot BvsH curve instead of IvsH.

When we replace a circular current-carrying loop with a magnetic dipole to resemble field lines of the circular loop, the pole strength m and the distance between the poles are not fixed.
But the magnetic dipole moment of both systems is always fixed. It is the product of the magnetic moment and the distance between the poles. In other words, md is fixed.
A current loop of area $A$ and current $I$ can be replaced with a magnetic dipole of dipole moment md.
i.e. md $= IA$

They always form complete closed loops. Unlike lines of electric flux which radiate from and terminate at the charged surfaces, lines of magnetic flux exist all the way through the magnet.
They behave as if they are elastic. That is, when distorted they try to return to their natural shape and spacing.
The lines of force of magnetic field are radiated from the north $(N)$ pole to the south $(S)$ pole.
Flux lines do not cross or interact to each other.
The density of lines of magnetic force indicates the strength of field at the point. Since strength is greatest at the poles, the magnetic lines of force are crowded there.

The magnetic field lines of the earth resemble that of a hypothetical magnetic dipole located at the centre of the earth.
The axis of the dipole does not coincide with the axis of rotation of the earth and it is tilted at some angle $($angle of declination$)$. Here in this situation the angle of declination is approximately $11.3^\circ $ with respect to the later. Here two possibilities arises as shown in the figure below.

The $SI$ unit of magnetic flour is weber.
It is expressed as $W b= kg \cdot M ^2 S^{-2} A^{-1}$

Partially filled inner sub-shells, due to the magnetic moment of unpaired electrons in partially filled inner sub$-$shells which got align in a particular direction in the presence of external magnetic field.

From the Curie’s law explains, $\text{I}\propto\frac{\text{B}}{\text{T}}$
Here, $B$ is magnetic field induction, $I$ is the intensity of magnetisation and $T$ is absolute temperature.
$\Rightarrow\ \Big(\frac{\text{I}_2}{\text{I}_1}\Big)=\Big(\frac{\text{B}_2}{\text{B}_1}\Big)\times\Big(\frac{\text{T}_1}{\text{T}_2}\Big)$
Given,
$I _1=8 Am ^{-1}, B_1=0.6 T, T _1=4 K, B _2=0.2 T, T _2=16 K, I _2=?$
By putting values in equation $…(i),$ we have,
$\text{I}_2=\Big(\frac{2}{3}\Big)\text{Am}^{-1}.$

$\overrightarrow{\text{H}}=\frac{\overrightarrow{\text{B}}}{\mu_0}=\frac{1}{4\pi}\frac{\text{id}\overrightarrow{\text{l}}\times\overrightarrow{\text{r}}}{\text{r}^3}$
The value of $H$ at $P$ will remain almost constant.

Diamagnetic sultance
$-1 \leq χ<0$
$\theta =\mu <1$
$χ=$ susceptibility

Bell laboratory has developed superconductor at a temperature of $40 K$.Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April $8, 1911$, in Leiden.

Magnetic susceptibility of a ferromagnetic material is very very greater than $1$, that of diamagnetic material is negative whereas that of a paramagnetic material is small and positive.
Hence, the given material is a ferromagnetic material.