Magnetism And Matter

Question

A short bar magnet of magnetic moment 5.25 x 10^–2 JT^–1 is placed with its axis perpendicular to earth's field direction. At what distance from the centre of the magnet, is the resultant field inclined at 45° with earth's field on (i) its normal bisector, (ii) its axis? Magnitude of earth's field at the place 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

Solution

Here, a bar magnet is placed with it's axis perpendicular to the earth's field direction.
Magnetic moment, M = 5.25 x 10^–2 JT^–1
Earth's field

\vec{B_{e}} = 0.42 G = 0.42 \times 10^{- 4} T

(i) At a point P which is at a distance r from normal bisector [shown in fig. (a)], we will find the resultant magnetic field on it's normal bisector.

Therefore,

Magnetic field B₂ due to magnet at equitorial line is,

\vec{B_{2}} = \frac{μ_{0}}{4 π} \frac{M}{r^{3}}

, along PA || NS .

The resultant field

\vec{R}

will be inclined at 45° to the earth's field along PQ’, only when

|\vec{B_{2}}| = |\vec{B_{e}}|

\frac{μ_{0}}{4 π} \frac{M}{r^{3}} = 0.42 \times 10^{- 4}

\frac{10^{- 7} \times 5.25 \times 10^{- 2}}{r^{3}} = 0.42 \times 10^{- 4}

which gives, r = 0.05 m = 5 cm.

(ii) When the point P lies on axis of the magnet such that OP = r, field due to magnet [Fig. (b),] is given by,

\vec{B_{1}} = \frac{μ_{0}}{4 π} \frac{2 M}{r^{3}},

along PO.

Earth's field

\vec{B_{e}}

is along

\vec{PA} .

The resultant field

\vec{R}

will be inclined at 45° to earth's field only when,

|\vec{B_{1}}| = |{\vec{B}}_{e}|

∴

\frac{μ_{0}}{4 π} \frac{2 M}{r^{3}} = 0.42 \times 10^{- 4}

which gives

r = 6.3 \times 10^{- 2} m = 6.3 cm .

Some More Questions From Magnetism and Matter Chapter

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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?

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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?

A bar magnet of magnetic moment 1.5 JT^–1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?
(b) What is the torque on the magnet in cases (i) and (ii)?

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Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

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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NCERT Sample Papers

Entrance Exams Preparation

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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: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:
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?