The Earth S Magnetism

To correctly answer this question about the properties of paramagnetic substances, let's break down each statement:

1. Statement A: Align themselves along the directions of external magnetic field.
   Paramagnetic substances have unpaired electrons that cause them to have a net magnetic moment. When placed in an external magnetic field, these substances tend to align themselves along the direction of the field. This statement is true.
2. Statement B: Attract strongly towards external magnetic field.
   While paramagnetic substances are attracted towards the magnetic field, they do not attract strongly. Strong attraction is a characteristic of ferromagnetic substances. Thus, this statement is false for paramagnetic substances.
3. Statement C: Has susceptibility little more than zero.
   The magnetic susceptibility of paramagnetic materials is positive but small, meaning it is slightly more than zero. This property confirms that paramagnetic substances weakly respond to magnetic fields. Thus, this statement is true.
4. Statement D: Move from a region of strong magnetic field to weak magnetic field.
   Paramagnetic substances tend to move from a region of weak magnetic field to a region of strong magnetic field, not the other way around. Therefore, this statement is false.

Based on the above analysis, statements A and C are correct. Therefore, the most appropriate answer is A, C Only.

To determine the value of for the torsional constant of the suspension wire, we begin by considering the dynamics of a moving coil galvanometer. The torque on the coil due to current is given by:

where is the number of turns, is the magnetic field, is the area of each turn, and is the current.
Substituting the given values: , , (converted from cm² to m²), and , we calculate:

The torsional constant relates the torque to the angular deflection as . Given radians, we substitute to find :

Solving for :

The torsional constant is expressed as , so equating to gives:

The problem asks for the magnetic force per unit length experienced by a long, straight current-carrying conductor placed in the Earth's horizontal magnetic field.

Concept Used:

The magnetic force ( ) on a straight conductor of length carrying a current in a uniform magnetic field is given by the Lorentz force formula:

The magnitude of this force is given by:

where is the angle between the direction of the current (vector ) and the direction of the magnetic field ( ).

The force per unit length ( ) is therefore:

Step-by-Step Solution:

Step 1: Identify the given physical quantities.

• Magnitude of the horizontal component of Earth's magnetic field, .
• Current in the conductor, .

Step 2: Determine the directions and the angle between the current and the magnetic field.

The direction of the horizontal component of Earth's magnetic field ( ) is from geographic South to geographic North.

The direction of the current ( ) is from South-East (SE) to North-West (NW).

Let's visualize these directions on a compass:

• The North direction is at .
• The North-West direction is at an angle of to the West of North.

Therefore, the angle ( ) between the direction of the magnetic field (North) and the direction of the current (North-West) is .

Step 3: Substitute the known values into the formula for force per unit length.

Final Computation & Result:

Step 4: Calculate the numerical value.

We know that .

The terms cancel out.

The problem asks for the answer to be expressed in the form .

The force per unit length experienced by the conductor is 35 .