Magnetism And Matter

Given:

• Number of turns in toroid,
• Current through wire,
• Magnetic susceptibility,
• Magnetization,

Step 1: Relate Magnetization to Magnetic Field

Magnetization ( ) is given by:

where is the magnetic field intensity.

Solving for :

Step 2: Express for a Toroid

For a toroid, the magnetic field intensity is:

where is the radius of the ring.

Step 3: Solve for Radius ( )

Substitute the known values into the equation for :

Simplify the equation:

Solve for :

Conclusion:

The radius of the ring is 20 cm.

Answer:

Given:

• Horizontal component of Earth's magnetic field ( ) = 0.36 Gauss
• Dip angle ( ) =

Step 1: Understand the Relationship Between Components

The Earth's total magnetic field ( ) can be resolved into horizontal ( ) and vertical ( ) components:

Step 2: Calculate the Total Magnetic Field ( )

Using the horizontal component formula:

Substitute the given values:

Conclusion:

The total magnetic field of the Earth at this location is 0.72 Gauss.

Answer:

Given:

• Initial turns per unit length,
• Final turns per unit length,
• Current ( ) is constant

Step 1: Magnetic Field Formula

The magnetic field inside a long solenoid is given by:

where is the permeability of free space, is the number of turns per unit length, and is the current.

Step 2: Calculate Initial and Final Fields

Initial magnetic field ( ):

Final magnetic field ( ):

Step 3: Determine Change in Field

The change in magnetic field ( ) is:

Substituting the values:

Step 4: Calculate Percentage Change

Percentage change in magnetic field:

Simplifying:

Conclusion:

The magnetic field inside the solenoid changes by 0.5%.

Answer:

Biot-Savart's law relates the magnetic field produced by a current-carrying wire. Ampere's circuital law is an alternative form of the Biot-Savart law, and it provides a relationship between the magnetic field and the electric current in a circuit.
The integral form of Ampere's law is: where:
- is the magnetic field,
- is the differential length element of the closed loop,
- is the enclosed current,
- is the permeability of free space.
Hence, the correct answer is (D).