A magnet is suspended so that it may oscillate in the horizontal plane. It performs 20 oscillations per minute at a place where the angle of dip is 30° and 15 oscillations per minute, where the angle of dip is 60°. Compare the earth’s total magnetic field at these two places.

Solution

Magnet is suspended such that it oscillates in horizonal plane.
When, angle of dip is 30^o , magnet performs 20 oscillations per minute.
and,
When angle of dip is 60^o , it performs 15 oscillations per minute.

Frequency of oscillation is given by, $v = \frac{1}{2 π} \sqrt{\frac{{MB}_{H}}{I}}$

$or v \propto \sqrt{B_{H}} ω^{2} = \frac{MB}{I}$

$4 π^{2} v^{2} = \frac{MB}{I}$ [ $ω = 2 πν$ ]

Therefore,

$v = \frac{1}{2} π \sqrt{\frac{MB}{I}}$

$v \propto \sqrt{B \cos δ}$

$B \cos δ \propto v^{2} B \propto \frac{v^{2}}{\cos δ}$

Hence, the ratio of Earth's magnetic field at these two places is
$\frac{B_{1}}{B_{2}} = \frac{v_{1}^{2}}{\cos δ_{1}} \times \frac{\cos δ_{2}}{v_{2}^{2}} = \frac{20 \times 20 \times \cos 60 °}{\cos 30 ° \times 15 \times 15}$

$= \frac{200 \times 2}{\sqrt{3} \times 225} = \frac{400}{225 \sqrt{3}} = \frac{16}{9 \sqrt{3}}$

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:
Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:
The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

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Magnetism And Matter

A magnet is suspended so that it may oscillate in the horizontal plane. It performs 20 oscillations per minute at a place where the angle of dip is 30° and 15 oscillations per minute, where the angle of dip is 60°. Compare the earth’s total magnetic field at these two places.

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:
Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:
The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

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For Daily Free Study Material Join wiredfaculty

Magnetism And Matter

A magnet is suspended so that it may oscillate in the horizontal plane. It performs 20 oscillations per minute at a place where the angle of dip is 30° and 15 oscillations per minute, where the angle of dip is 60°. Compare the earth’s total magnetic field at these two places.

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Answer the following question regarding earth:
Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:
The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?