Magnetism And Matter

Step 1: Understanding the Concept:
Curie's law describes the magnetic behavior of paramagnetic materials in relation to temperature. Paramagnetic materials are weakly attracted to magnetic fields. This attraction is due to the presence of unpaired electrons, which act as tiny magnetic dipoles.
Step 2: Key Formula or Approach:
The law is mathematically expressed in terms of magnetic susceptibility ( ) or magnetization ( ).
The magnetic susceptibility is defined as the ratio of the intensity of magnetization ( ) to the magnetic field intensity ( ).
Curie's Law states:
or where:
- is the magnetic susceptibility.
- is the absolute temperature in Kelvin.
- is a material-specific constant called the Curie constant.
Step 3: Detailed Explanation:
In paramagnetic materials, the atomic dipoles are randomly oriented due to thermal agitation. When an external magnetic field is applied, it tends to align these dipoles, causing a net magnetization.
However, the thermal energy of the atoms opposes this alignment. As the temperature increases, thermal agitation becomes stronger, making it harder for the external field to align the dipoles. Consequently, the material's ability to be magnetized (its susceptibility) decreases.
Curie's law quantifies this relationship, stating that the susceptibility is inversely proportional to the absolute temperature. This means that if you double the absolute temperature, you halve the magnetic susceptibility of a paramagnetic substance, assuming the applied field is not too strong.
Step 4: Final Answer:
Curie's law is a fundamental principle in magnetism that relates the magnetic susceptibility of a paramagnetic material to its absolute temperature, showing they are inversely proportional.

Step 1: Understanding the Concept:
The Earth behaves like a large magnet with a magnetic field extending into space. This magnetic field is generated by the motion of molten iron alloys in its outer core. The strength of this magnetic field is quantified by its magnetic dipole moment. This is a factual, standard value in physics.
Step 2: Detailed Explanation:
The magnetic moment of the Earth has been measured through various geophysical methods. The currently accepted approximate value for the Earth's magnetic dipole moment is about Joules per Tesla (J T ).
The unit J T is equivalent to Ampere-meter squared (A m ), which is the standard SI unit for magnetic moment.
Let's check the options:
(A), (B), and (C) present values that are drastically different in magnitude from the known value.
(D) provides the correct order of magnitude and the standard value for the Earth's magnetic moment.
Step 3: Final Answer:
The accepted value for the magnetic moment of the Earth is approximately J T . Therefore, option (D) is correct.

Step 1: Understanding the Concept:
Materials are classified based on their behavior in an external magnetic field. The main categories are diamagnetic, paramagnetic, and ferromagnetic.
Step 2: Detailed Explanation:
- Diamagnetic materials are weakly repelled by a magnetic field. They have a magnetic permeability slightly less than that of a vacuum. Examples include water, copper, and bismuth.
- Paramagnetic materials are weakly attracted to a magnetic field. They have a magnetic permeability slightly greater than that of a vacuum. Examples include aluminum, platinum, and oxygen.
- Ferromagnetic materials are very strongly attracted to a magnetic field and can be permanently magnetized. They have a very high magnetic permeability. The atoms in these materials have magnetic moments that align in large regions called domains.
Nickel (Ni) is one of the three common elements, along with Iron (Fe) and Cobalt (Co), that exhibit ferromagnetism at room temperature.
Step 3: Final Answer:
Nickel is a ferromagnetic material. Therefore, option (C) is correct.

Step 1: Understanding the Concept:
Just as electric charges create electric fields, moving charges (currents) or intrinsic properties of particles (like electron spin) create magnetic fields. The magnetic moment is the fundamental quantity that characterizes the source of this magnetic field. It determines the torque the object will experience in an external magnetic field.
Step 2: Detailed Definition:
The magnetic dipole moment, often simply called magnetic moment (symbol or ), quantifies the magnetic strength of a dipole.
- For a Bar Magnet: It is a vector that points from the south pole to the north pole of the magnet. Its magnitude is the product of the pole strength and the magnetic length.
- For a Current Loop: A planar loop of wire carrying a current with an enclosed area has a magnetic moment with magnitude . The direction of the magnetic moment vector is perpendicular to the plane of the loop, given by the right-hand grip rule (if you curl the fingers of your right hand in the direction of the current, your thumb points in the direction of ).
The torque experienced by an object with magnetic moment in an external magnetic field is given by .
Step 3: S.I. Unit and Dimension:
S.I. Unit:
Using the formula for a current loop, :
- The S.I. unit of current ( ) is Ampere (A).
- The S.I. unit of area ( ) is meter squared (m ).
Therefore, the S.I. unit of magnetic moment is Ampere-meter squared (A m ).
An equivalent unit is Joules per Tesla (J/T).
Dimension:
- The dimension of current ( ) is [A].
- The dimension of area ( ) is [L ].
Therefore, the dimensional formula for magnetic moment is [L A].
Step 4: Final Answer:
The magnetic moment is a measure of an object's magnetic properties. Its S.I. unit is A m and its dimension is [L A].

Step 1: Understanding the Concept:
The Earth's total magnetic field ( ) at any point can be resolved into two components: a horizontal component ( ) and a vertical component ( ). The angle that the total magnetic field vector makes with the horizontal direction is called the angle of dip or inclination ( ).
Step 2: Key Formula or Approach:
The relationship between the components and the angle of dip ( ) is given by trigonometry:
Step 3: Detailed Explanation:
We are given the following relationship in the problem:
The horizontal component ( ) is times the vertical component ( ).
Mathematically, this is written as:
Now, we substitute this into the formula for the angle of dip:
The term cancels out from the numerator and the denominator:
To find the angle , we take the inverse tangent (arctan) of both sides:
From our knowledge of standard trigonometric values, we know that .
Therefore, the angle of dip is:
Step 4: Final Answer:
The value of the angle of dip at that place is 30 .