Magnetism And Matter

Question

The core of a toroid having 3000 turns has inner and outer radii of 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.70 A is 2.5 T. What is the relative permeability of the core? Take $π$ = 3.14.

Solution

Number of turns of torroid, N = 3000
Inner radii, r₁ = 11 cm
Outer radii, r₂ = 12 cm
Therefore, mean radius, r =11.5 cm = 11.5 x 10^–2 m
Magnetic field in the coil, B= 2.5 T
Current carried by the coil, I = 0.70 A

The magnetic field in the empty space enclosed by the windings of the toroid is given by

B = μ_{0} nI

...(1)

where, n is the number of turns per unit length and I is the current.

If the space is filled by a core of permeability μ, then equation (1) is rewritten as :

B = μnI

Hence,

Number of turns per unit length is,

n = \frac{3000}{2 π \times 11.5 \times 10^{- 2}} m^{- 1}

Here, we have ignored the variation of B across the cross-section of the toroid and taken the radius of the toroid to be the mean of inner and outer radii.

∴

μ = \frac{B}{nI} = \frac{2.5 \times 2 π \times 11.5 \times 10^{- 2}}{3000 \times 0.7} μ = 8.6 \times 10^{- 4} T m A^{- 1}

Relative permeability of core,

μ_{r} = \frac{μ_{0}}{μ_{0}} = 684.7

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Magnetism And Matter

The core of a toroid having 3000 turns has inner and outer radii of 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.70 A is 2.5 T. What is the relative permeability of the core? Take $π$ = 3.14.

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

The core of a toroid having 3000 turns has inner and outer radii of 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.70 A is 2.5 T. What is the relative permeability of the core? Take π = 3.14.

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

The core of a toroid having 3000 turns has inner and outer radii of 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.70 A is 2.5 T. What is the relative permeability of the core? Take $π$ = 3.14.

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?