**11 Magnetic Materials**

**Multiple Choice Questions**

**1. If a watch-glass containing a small quantity of water is placed on two dissimilar magnetic poles, then water**

(A) shows a depression in the middle.

(B) shows an elevation in the middle.

(C) surface remains horizontal.

(D) evaporates immediately.

**Ans.** (A) shows a depression in the middle.

**2. Soft iron is used to make the core of transformer because of its**

(A) low coercivity and low retentivity

(B) low coercivity and high retentivity

(C) high coercivity and high retentivity

(D) high coercivity and low retentivity

**Ans.** (A) low coercivity and low retentivity

**Theory Questions**

**11.2 Torque Acting on a Magnetic Dipole in a Uniform Magnetic Field**

**State the formula for magnetic potential energy of a dipole and hence obtain the minimum and maximum magnetic potential energy.**

**Ans:**

i. Magnetic potential energy of a dipole:

ii. Special cases:

a. Minimum magnetic potential energy:

b. Maximum magnetic potential energy:

**11.3 Origin of Magnetism in Materials**

**Show that the orbital magnetic dipole moment of a revolving electron is****.**

**Ans:** Expression for magnetic dipole moment:

i. Consider an electron of mass and charge revolving in a circular orbit of radius around the positive nucleus in clockwise direction, leading to an anticlockwise current.

ii. – If the electron travels a distance in time then, its orbital speed

iii. Magnitude of circulating current is given by,

But,

iv. The orbital magnetic moment associated with orbital current loop is given by,

( Area of current loop, )

**In a hydrogen atom, an electron carrying charge ‘****‘ revolves in an orbit of radius ‘****‘ with speed ‘****‘. Obtain an expression for the magnitude of magnetic moment of a revolving electron.**

**Ans:** Refer Subtopic 11.3: Q. No. 1

**Derive an expression for orbital magnetic moment of an electron revolving around the nucleus in an atom.**

**OR**

**Derive an expression for magnitude of magnetic dipole moment of a revolving electron.**

**Ans:** Refer Subtopic 11.3: Q. No. 1

- What is gyromagnetic ratio? Write the necessary expression.

[July 22]

Ans:

i. The ratio of magnetic dipole moment with angular momentum of revolving electron is called the gyromagnetic ratio.

ii. Gyromagnetic ratio is given by,

**Write the mathematical formula for Bohr magneton for an electron revolving in****orbit.**

**OR**

**State the formula for the Bohr magneton.**

**Ans:** Formula for Bohr Magneton

**11.4 Magnetization and Magnetic Intensity**

**Define magnetization. State its formula and S.I. unit.**

**Ans:**

i. Definition:

The ratio of magnetic moment to the volume of the material is called magnetization.

It is denoted by .

ii. If magnetic specimen of volume ‘ ‘ acquires net magnetic dipole moment ‘ ‘ due to the magnetising field, then

iii. It is a vector quantity.

iv. Unit: in SI system.

v. Dimensions:

**What is magnetization?**

**Ans:** Refer Subtopic 11.4: Q. No. 1

**Define magnetization.**

**Ans:** Refer Subtopic 11.4: . No. 1 (Definition only)

**Define magnetization. Write its SI unit and dimensions.**

**Ans:** Refer Subtopic 11.4: Q. No. 1 [(i), (iv) and (v)]

**What is magnetization, magnetic intensity and magnetic susceptibility?**

**Ans:**

i. Refer Subtopic 11.4: Q. No. 1 (Definition only)

a Magnetic intensity: The ratio of the strength of magnetising field to the permeability of free space is called as magnetic intensity.

-2. Magnetic susceptibility: The ratio of magnitude of intensity of magnetization to that of magnetic intensity is called as magnetic susceptibility.

**Define and state unit and dimensions of :**

**i. Magnetization**

**I. Magnetic susceptibility**

**Ans:**

i. Refer Subtopic 11.4: Q. No. 1 [(i), (iv) and (v)]

ii. Refer Subtopic 11.4: Q. No. 5 (iii)

Magnetic susceptibility is unitless and dimensionless quantity.

**11.5 Magnetic Properties of Materials**

**Explain ferromagnetism on the basis of domain theory.**

**Ans: **Domain theory:

i. In ferromagnetic materials, interaction called exchange coupling or exchange interaction between neighbouring magnetic dipole moments is strong.

ii. Due to this interaction, small regions called domain are formed in which all the atoms have their magnetic moments aligned in the same direction. The common direction of magnetic moment is called the domain axis. Domain size can be a fraction of a millimetre and contains about atoms.

iii. The boundary between adjacent domains with a different orientation of magnetic moment is called a domain wall.

iv. In unmagnetized state, even though the magnetic moment of individual domains are non-zero, the domain axes of different domains being oriented randomly, the net magnetic moment of the whole material is zero.

(a)

(b)

Unmagnetised (a) and magnetised (b) ferromagnetic material with domains

v. When an external magnetic field is applied, flipping or domain rotation occurs. In this process, domains try to align themselves along the direction of the applied magnetic field. The number of domains aligning in that direction increases as magnetic field is increased.

vi. When sufficiently high magnetic field is applied, all the domains coalesce together to form a giant domain as shown in figure.

vii. When the strong external magnetic field is completely removed, the domain boundaries are not set back to original position resulting in the net magnetic moment remaining non-zero and the ferromagnetic material is said to retain magnetization. Such materials are used in preparing permanent magnets.

viii. In non-uniform magnetic field, ferromagnetic material tends to move from weaker part to stronger part of the field.

**Give any ‘two’ points of differences between diamagnetic and ferromagnetic substances.**

**Ans:**

No. | Diamagnetic Substance | Ferromagnetic Substance |

i. | They are weaklyrepelled by magnet. | They are stronglyattracted by magnet. |

ii. | If a thin rod ofdiamagnetic substanceis freely suspended inuniform magnetic field,it comes to rest slowlywith its lengthperpendicular to thedirection of magneticfield. | If a thin rod offerromagneticsubstance is freelysuspended in a uniformmagnetic field, it comesquickly to restwith its length parallelto the direction of thefield. |

iii. | When placed in nonuniform magnetic field,they show a moderatetendency to move fromthe stronger to theweaker part of thefield. | When placed in nonuniform magnetic field,they show a strongtendency to move fromthe weaker to thestronger part of thefield. |

iv. | In the absence ofexternal magneticfield, the resultantmagnetic moment ofeach atom is zero. | The resultant magneticmoment of each atomof a ferromagneticsubstance is muchgreater than zero. |

v. | There is no effect oftemperature ondiamagnetic substance. | There is effect oftemperatureferromagneticsubstance. |

vi. | They cannotpermanentlymagnetised. | They can bepermanentlymagnetised. |

[Any two points]

**Distinguish between ‘paramagnetic’ and ‘ferromagnetic’ substances.**

**[Mar 16]**

Ans:

No. | Parangagicticsubstance | Ferromagnetic Substance |

i. | It is weakly attractedby a magnet. | It is strongly attractedby a magnet. |

ii. | When kept in a non-uniform magnetic field,it shows moderatetendency to move fromweaker to the strongerpart of the field. | When kept in a non-uniform magnetic field,it shows strongtendency to move fromweaker to the strongerpart of the field. |

**Draw the diagrams showing the dipole moments in paramagnetic substance when external magnetic field is****i. absent****ii. strong.**

**Ans:**

Strong external magnetic field

**Distinguish between diamagnetic and paramagnetic substances.**

**Ans:**

110. | ||

i. | In an externalmagnetic field, asubstance gets weaklymagnetised in thedirection opposite tothat of the field. | In an externalmagnetic field, aparamagneticsubstance gets weaklymagnetised in thesame direction as thatof the field. |

ii. | When placed in a non-uniform magnetic field,it tends to move fromthe stronger to theweaker part of the field. | When placed in a non-uniform magnetic field,it tends to move fromthe weaker to thestronger part of thefield. |

iii. | It is weakly repelledby a magnet. | It is weakly attractedby a magnet. |

iv. | Magnetic moment ofevery atom of adiamagnetic substanceis zero. | Every atom of aparamagnetic substanceis a magnetic dipolehaving a certainresultantmoment. magnetic |

v. | When a rod ofdiamagnetic substanceis suspended in auniform magnetic field,it comes to rest with itslength perpendicular tothe direction of thefield. | When a rod ofparamagnetic substanceis suspended in auniform magnetic field,it comes to rest with itslength parallel to thedirection of the field. |

vi. | There is no effect oftemperature ondiamagnetic substance. | There is effect oftemperature on onparamagnetic substance. |

**What is Curie temperature and what happens above Curie temperature? [July 18]**

**Ans:**

i. The temperature at which a ferromagnetic material transforms into a paramagnetic substance is called Curie temperature of that material.

ii. An increase in the temperature of a ferromagnetic material weakens the exchange coupling between neighbouring moments which results in the domain structure getting distorted.

iii. Above Curie temperature the domain structure of a ferromagnetic material collapses totally and the material behaves like paramagnetic material.

**What happens to a ferromagnetic substance heated above Curie temperature? [Mar 19]**

**Ans:** When heated above Curie temperature, ferromagnetic substances become paramagnetic substances

**What happens if the rod of dia-magnetic material is placed in a non-uniform magnetic field?**

**Ans.** When the rod of diamagnetic material is placed in a non-uniform magnetic field, it tends to move from stronger part to the weaker part of the magnetic field.

**11.3 Origin of Magnetism in Materials**

**1 A electron in an atom revolves around the cless in an orbit of radius ****. If the frequency of revolution of an electron is ****, calculate the orbital angular cocotam.**

[Given: Charge on an electron ; Gyromagnetic ratio

**Solution:**

Given:

To find: Angular momentum

Formula:

Calculation: Since, and

Using formula,

Ans: The orbital angular momentum of the electron is .

**A circular coil of 300 turns and diameter****carries a current of****. Calculate the magnitude of the magnetic dipole moment associated with the coil.**

**Solution:**

Given:

To find: Magnetic dipole moment

Formula:

Calculation: From formula,

Ans: The magnitude of the magnetic dipole moment associated with the coil is

**An electron in an atom is revolving round the nucleus in a circular orbit of radius****with a speed of****. Find the angular momentum of electron.**

**Solution:**

To find: Angular momentum of electron (L)

Formula:

Calculation: From formula,

Ans: Angular momentum of electron is .

**11.4 Magnetization and Magnetic Intensity**

**The magnetic susceptibility of annealed iron at saturation is 4224 . Find the permeability of annealed iron at saturation.****SI unit).**

**Solution:**

Given:

To find: Permeability

Formula:

Calculation: From formula,

antilog

Ans: The permeability of annealed iron at saturation is .

**The magnetic moment of a magnet of dimensions****is****. Calculate the intensity of magnetization.**

**Solution:**

Given:

To find: Intensity of magnetization

Formula:

Calculation: sing formula,

Ans: The intensity of magnetization is .

**An iron rod of area of cross-section****is subjected to a magnetising field of****. Calculate the magnetic permeability of the iron rod. [Magnetic susceptibility of iron****, magnetic permeability of vacuum****S. I. unit**

**Solution:**

**Given:**

To find: . Permeability

Formula:

Calculation: From formula

Ans: The magnetic permeability of the iron rod is .

**Find the magnetization of a bar magnet of length****and cross-sectional area****, if the magnetic moment is****. [July 17]**

**Solution:**

Given:

To find: magnetisation

Formula:

Calculation: Since, cross sectional area

From formula,

Ans: The intensity of magnetisation is .

**11.5 Magnetic Properties of Materials**

**The susceptibility of magnesium at****is****. At what temperature will the susceptibility increase to****? [Mar 14]**

**Solution:**

Given:

To find: Required temperature

Formula: constant

Calculation: From formula,

Ans: The temperature at which the susceptibility will increase to is .

**The susceptibility of magnesium at****is****. At what temperature will the susceptibility decrease by****?**

**Solution:**

Given:

To find: Required temperature

Formula: constant

Calculation: From formula,

Ans: The required temperature is .

**The susceptibility of magnesium at****is****. At what temperature will the susceptibility increase to****?**

**Solution:**

Given:

To find: Required temperature

Formula: constant

Calculation: From formula,

Ans: The required temperature is .

**The susceptibility of magnetism at****is****. What will be its susceptibility at****?**

**Solution:**

Given:

To find: Susceptibility at temperature

Formula: constant

Calculation: From formula,

Ans: The susceptibility at is .

**5. The susceptibility of magnesium at **** is ****. At what temperature the susceptibility will decrease by **** ?**

**Solution:**

Given:

To find: Temperature

Formula: constant

Calculation: From formula,

Ans: Required temperature is .