Magnetism And Matter

Question

A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude 5.0 x 10^–2 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s^–1. What is the moment of inertia of the coil about its axis of rotation?

Solution

Given,
Number of turns in the coil, N = 16
Radius of the coil, r = 10 cm = 0.1 m
Current passing thropugh the coil, I = 0.75 A
External magnetic field, $B = 5.0 \times 10^{- 2} T$
Frequency of oscillation, $ν = 2.0 s^{- 1}$
Magnetic moment is given by, M= NIA

Therefore,
M = NI ${πr}^{2}$
= $16 \times 0.75 \times \frac{22}{7} (0.1)^{2}$
= 0.377 JT^-1

Now, using formula $ν = \frac{1}{2 π} \sqrt{\frac{MB}{I}}$

$∴$ $v^{2} = \frac{MB}{4 π^{2} I}$

$I = \frac{MB}{4 π^{2} ν^{2}}$
Putting values, we get

$I = \frac{0.377 \times 5.0 \times 10^{- 2}}{4 \times {(\frac{22}{7})}^{2} \times 2^{2}} = 1.2 \times 10^{- 4} kg m^{2}$

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Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:
The angle of dip at a location in southern India is about 18°. Would you expect a greater or smaller dip angle in Britain?

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:The angle of dip at a location in southern India is about 18°. Would you expect a greater or smaller dip angle in Britain?

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:
The angle of dip at a location in southern India is about 18°. Would you expect a greater or smaller dip angle in Britain?

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?