The magnetic moment of a short bar magnet is 1.6 m². It is placed in the magnetic meridian with north pole pointing south. The neutral point is obtained at 20 cm from the centre of the magnet. Calculate the horizontal component H of earth's field. If magnet be reversed i.e., north pole pointing north, find the position of the neutral point.

Solution

Here,
Magnetic moment, M = 1.6 A m²
Neutral point is obtained at d₁ = 20 cm = 0.2 m
Horizontal component of earth's magnetic field, H = ?

When north pole of magnet is pointing south, neutral points lie on axial line of magnet.
At neutral point,

   $B_{ax} = \frac{μ_{0}}{4 π} \frac{2 M}{d_{1}^{3}} = H$

$H = \frac{10^{- 7} \times 2 \times 1.6}{(1 / 5)^{3}} = 4 \times 10^{- 5} tesla .$
Now,
When magnet is reversed i.e., north pole is pointing north, neutral points lie on equatorial line of the magnet.

We have to calculate d₂i.e., the position where is the neutral point is obtained.

As,    $B_{eq} = \frac{μ_{0}}{4 π} \frac{M}{d_{2}^{3}} = H$

$∴$    ${d_{2}}^{3} = \frac{μ_{0}}{4 π} \frac{M}{H}$

${d_{2}}^{3} = \frac{10^{- 7} \times 1.6}{4 \times 10^{- 5}} = 0.4 \times 10^{- 2} m^{3} = 0.4 \times 10^{- 2} \times 10^{6} {cm}^{3} = 4000 {cm}^{3}$

$d_{2} = (4000)^{1 / 3} = 15.87 cm .$

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Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:
If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

Answer the following question regarding earth:
In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

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

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth: If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

Answer the following question regarding earth:In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

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:
If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

Answer the following question regarding earth:
In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

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?