Problem 24 - Master Resource Book in JEE Main Physics

Question

Let the magnetic field on the earth be modelled by that of a point magnetic dipole at the centre of the earth. The angle of dip at a point the geographical equator (a) is always zero (b) can be zero at specific points (c) can be positive or negative (d) is bounded

Step-by-Step Solution

Answer

(b) can be zero at specific points.

Step 1: Understanding the Angle of Dip

The angle of dip, or magnetic inclination, is the angle made with the horizontal by the Earth's magnetic field lines. At the magnetic equator, the field lines are perfectly horizontal, so the angle of dip is zero. This means any point on the geographical equator, where the magnetic equator exists, will also have a zero angle of dip.

Step 2: Analyzing the Options

Let’s consider each answer choice: (a) is always zero - suggesting the angle of dip is zero everywhere on the equator. (b) can be zero at specific points - indicating that there are specific points where the angle is zero. (c) can be positive or negative - suggesting the angle varies along the equator. (d) is bounded - implying limits but not necessarily zero. Since the angle of dip is precisely zero at specific places on the equator where the magnetic equator meets the geographical equator, (b) is correct.

Step 3: Selecting the Correct Option

The angle of dip will be zero at specific points along the geographical equator where it coincides with the magnetic equator. Therefore, some places have zero dip, not everywhere along the equator, making option (b) the right choice.

Key Concepts

Magnetic Field

The concept of a magnetic field is crucial in understanding many physical phenomena, including the Earth's magnetism. A magnetic field is a vector field that exerts force on charged particles in motion, leading to phenomena like magnetization and electromagnetic induction. In mathematical terms, it is represented by the symbol \( \mathbf{B} \) and described by both magnitude and direction.

Magnetic fields originate from magnetic dipoles or changing electric fields. They are depicted using field lines that indicate direction and strength. The closer the lines, the stronger the field.

• In the Earth’s context, its field resembles that produced by a giant bar magnet tilted about 11 degrees from the rotation axis.
• This field influences navigation systems and migratory behavior in many species.
• Understanding magnetic fields helps us grasp significant concepts like the magnetic compass and auroras.

Magnetic Dipole

A magnetic dipole refers to a magnetic north and south pole separated by a small distance, resembling in many ways a tiny bar magnet. Every magnet possesses a magnetic dipole. The Earth's overall magnetic field can be imagined as a giant dipole located at its center, showing how strong dipoles influence surrounding fields.

The direction of this dipole is from the south magnetic pole to the north magnetic pole. The strengths of these poles, or the magnetic moment \( \mathbf{M} \), determines the intensity of the field.

• The Earth’s magnetic moment has a role in determining our magnetic field strength globally.
• It is essential for aligning compass needles with Earth's poles.
• The concept of magnetic dipoles forms the foundation for technologies like MRIs and electric motors.

Geographic Equator

The geographic equator is an imaginary line encircling the Earth equidistant from the poles. It divides the Earth into the Northern and Southern Hemispheres. Known for its constant equidistance from the poles, the equator serves as a significant geographical marker.

While primarily a geographic concept, it plays a role in understanding Earth's magnetic properties thanks to its relation with the magnetic equator.

• The geographic equator's importance also extends to climate variations, marking the region where sunlight is distributed most evenly across the year.
• Unlike the magnetic equator, the geographic equator is fixed.
• It is often used as a reference point for mapping and navigation.

Magnetic Equator

The magnetic equator is a vital concept in understanding the Earth’s magnetism, represented as a band encircling the Earth where the magnetic field is horizontal. Unlike the geographic equator, the magnetic equator is not fixed, as it shifts due to the dynamic nature of the Earth’s core and surrounding forces.

At the magnetic equator, the angle of dip is zero, crucial for phenomena like the construction of magnetic anomaly maps.

• This line is critical when examining the link between Earth's inner dynamics and magnetic field behavior.
• The magnetic equator's shifting nature provides insights into the Earth's geophysical processes.
• It plays a significant role in radio signal propagation and satellite navigation.

Earth's Magnetism

Earth's magnetism is a fundamental geophysical feature caused by movements within the liquid outer core, consisting of iron and nickel. This generates a magnetic field emanating outward, which affects various Earth systems and space weather patterns.

Earth's magnetic field protects the planet from solar wind, a stream of charged particles from the sun.

• This natural shield deflects harmful particles, fostering conditions vital for life.
• The magnetic poles and equator derived from Earth's magnetism support navigation and wildlife migration.
• Earth's magnetism is also responsible for phenomena like auroras and the stability of satellite operations.

Understanding this concept not only aids in appreciating the complexity of our planet's inner workings but also underscores the interconnection between Earth's core and surface systems.