Magnetism And Matter

Question

A small magnet of magnetic moment $π$ x 10^–10 Am² is placed on the Y-axis at a distance of 0.1 m from the origin with its axis parallel to the X-axis. A coil having 169 turns and radius 0.05 m is placed on the X-axis at a distance of 0.12 m from the origin with the axis of the coil coinciding with X-axis. Find the magnitude and direction of the current in the coil for a compass needle placed at the origin to point in the north-south direction.

Solution

Given,
Magnetic moment, M =

π

x 10^–10 Am²Distance of magnet from origin at y-axis = 0.1 m
Number of tuns of coil, N = 169
Radius of the coil, r = 0.05 m
Distance of coil from origin at x-axis, x = 0.12 m

The compass needle placed at the origin will point in the north-south direction if the magnetic field placed at the origin, produced by the magnet and the coil are equal in magnitude and opposite in direction.

Magnetic field, at the origin, due to the magnet is given by

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

B_{m} = \frac{10^{- 7} \times π \times 10^{- 10}}{0.1 \times 0.1 \times 0.1} T

B_{m} = π \times 10^{- 14} T

(equitorial line)

Now,
The magnetic field B_c due to the circular coil should be opposite to

{\vec{B}}_{m} .

For this, the current through the coil should flow anticlockwise as seen from the origin.

Hence,

B_{C} = \frac{μ_{0} {NIr}^{2}}{2 {(r^{2} + x^{2})}^{3 / 2}} (axial line)

B_{C} = \frac{4 π \times 10^{- 7} \times 169 \times I \times (0.05)^{2}}{2 {[(0.05)^{2} + (0.12)^{2}]}^{3 / 2}} T

B_{C} = \frac{0.845 π \times 10^{- 7} \times I}{{[0.0025 + 0.0144]}^{3 / 2}}

B_{C} = \frac{0.845 π \times 10^{- 7} \times I}{{[\sqrt{0.0169}]}^{3}}

B_{C} = \frac{0.845 π \times 10^{- 7} \times I}{0.13 \times 0.13 \times 0.13}

i.e.,

= 3.84 π \times 10^{- 5} \times I

For needle to point in north-south direction

3.846 π \times 10^{- 5} \times I = π \times 10^{- 14}

\Rightarrow

I = \frac{10^{- 14}}{3.846 \times 10^{- 5}} A

= 2.6 \times 10^{- 10} A

Hence, as viewed from origin, the current flows in anti-clockwise direction.

Some More Questions From Magnetism and Matter Chapter

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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Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

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

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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: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:
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?