A solenoid of 500 turns per metre is carrying a current of 3A. Its core is made of iron, which has a relative permeability of 5000. Determine the magnitudes of magnetic intensity, magnetisation and magnetic field inside the core.

Solution

Given,
Number of turns in solenoid, n = 500
Current carried, I = 3A
Relative premeabiltiy of iron core, $μ_{r} = 5000$

Therefore,
Magnetic intensity,
$H = ni = 500 \times 3 = 1500 {Am}^{- 1}$

Using the relation between susceptibility and permeability,
$μ_{r} = 1 + χ_{cm}$

$∴$ $χ_{m} = μ_{r} - 1 = 5000 - 1 = 4999 \approx 5000$

Also, $μ_{r} = \frac{μ}{μ_{0}} = 5000$

$∴$ $μ_{r} = 5000 μ_{0}$

Magnetisation, $I = X_{m} H$

$= 5000 \times 1500 = 7.5 \times 10^{6} {Am}^{- 1}$

Magnetic field inside the core is given by,
$B = μH = 5000 μ_{0} H$ $∵ μ = μ_{0} H$ $= 5000 (4 π \times 10^{- 7}) \times 1500$

i.e., $B = 3 π = 3 \times \frac{22}{7} = 9.4 T .$

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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?

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Magnetism And Matter

A solenoid of 500 turns per metre is carrying a current of 3A. Its core is made of iron, which has a relative permeability of 5000. Determine the magnitudes of magnetic intensity, magnetisation and magnetic field inside the core.

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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Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Magnetism And Matter

A solenoid of 500 turns per metre is carrying a current of 3A. Its core is made of iron, which has a relative permeability of 5000. Determine the magnitudes of magnetic intensity, magnetisation and magnetic field inside the core.

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?