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The spokes of a wheel are made of metal and their lengths are of one metre. One rotating the wheel about its own axis in a uniform magnetic field of 5 × 10–6 tesla normal to the plane of the wheel a potential difference of 3.14 mV is generated between the rim and the axis. The rotational velocity of the wheel is (in rev/sec).
Correct answer is '20'. Can you explain this answer?
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Tesla, an emf of 5 volts is induced across the ends of each spoke.
To find the angular velocity of the wheel, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf is given by the equation:
emf = -N(dΦ/dt)
where emf is the induced electromotive force, N is the number of turns of the coil (in this case, the number of spokes), and dΦ/dt is the rate of change of magnetic flux through the coil.
In this case, the induced emf is given as 5 volts and the length of each spoke is given as 1 meter. Therefore, the number of turns of the coil is equal to the number of spokes, which is 1.
Substituting these values into the equation, we get:
5 = -(1)(dΦ/dt)
Simplifying the equation, we find:
dΦ/dt = -5 T/s
This means that the rate of change of magnetic flux through the spoke is -5 Tesla per second.
The angular velocity of the wheel can be calculated using the equation:
ω = dΦ/dt / A
where ω is the angular velocity, dΦ/dt is the rate of change of magnetic flux, and A is the area enclosed by the coil (in this case, the area enclosed by each spoke).
Since the spoke is assumed to be a straight line, the area enclosed by each spoke is zero. Therefore, the angular velocity of the wheel is:
ω = (-5 T/s) / 0 = undefined
In this case, the angular velocity of the wheel is undefined. This could be due to the assumption that the spokes are straight lines and do not enclose any area.
To find the angular velocity of the wheel, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf is given by the equation:
emf = -N(dΦ/dt)
where emf is the induced electromotive force, N is the number of turns of the coil (in this case, the number of spokes), and dΦ/dt is the rate of change of magnetic flux through the coil.
In this case, the induced emf is given as 5 volts and the length of each spoke is given as 1 meter. Therefore, the number of turns of the coil is equal to the number of spokes, which is 1.
Substituting these values into the equation, we get:
5 = -(1)(dΦ/dt)
Simplifying the equation, we find:
dΦ/dt = -5 T/s
This means that the rate of change of magnetic flux through the spoke is -5 Tesla per second.
The angular velocity of the wheel can be calculated using the equation:
ω = dΦ/dt / A
where ω is the angular velocity, dΦ/dt is the rate of change of magnetic flux, and A is the area enclosed by the coil (in this case, the area enclosed by each spoke).
Since the spoke is assumed to be a straight line, the area enclosed by each spoke is zero. Therefore, the angular velocity of the wheel is:
ω = (-5 T/s) / 0 = undefined
In this case, the angular velocity of the wheel is undefined. This could be due to the assumption that the spokes are straight lines and do not enclose any area.
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The spokes of a wheel are made of metal and their lengths are of one metre. One rotating the wheel about its own axis in a uniform magnetic field of5 × 10–6tesla normal to the plane of the wheel a potential difference of3.14mV is generated between the rim and the axis. The rotational velocity of the wheel is (inrev/sec).Correct answer is '20'. Can you explain this answer?
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