A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth’s magnetic field. The Earth’s magnetic field at the plane is 0.4 G and the angle of dip is 60°. Calculate the emf induced between the axle and the rim of the wheel. How will the value of emf be affected if the number of spokes were increased?

Solution

Emf induced in a rod of length ‘l’ with angular speed in a uniform magnetic field is given by,
$Error converting from MathML to accessible text.$

For earth’s magnetic field,

Horizontal component is given by,
$straight B subscript straight H space equals space open vertical bar straight B subscript straight l space end subscript close vertical bar cos space straight delta$

Vertical component is given by,
$straight B subscript straight V space equals space open vertical bar straight B subscript straight l close vertical bar space sin space straight delta$
Therefore, emf induced is given by,
$straight epsilon space equals space 1 half open vertical bar straight B subscript straight l close vertical bar space cos space straight delta space straight l squared space straight omega space space space equals space 1 half space straight x space 0.4 straight x space 10 to the power of negative 4 end exponent space cos space 60 to the power of straight o space straight x space left parenthesis 0.5 right parenthesis squared space straight x space 2 πν space space space space equals space 1 half straight x space 0.4 space straight x space 10 to the power of negative 4 end exponent space straight x space 1 half space straight x space left parenthesis 0.5 right parenthesis squared space straight x space 2 πν space straight x open parentheses space fraction numerator 120 space rev over denominator 60 space sec end fraction close parentheses space space space space equals space 10 to the power of negative 5 end exponent space straight x space 0.25 space straight x space 2 space straight x space 3.14 space straight x space 2 space space space space equals space 3.14 space straight x space 10 to the power of negative 5 end exponent space volt$

Emf induced is not dependent on the number of spokes.

Some More Questions From Magnetism and Matter Chapter

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?

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 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: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 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?