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Chapter 2: Problem 4

A conductor \(2 \mathrm{~m}\) long moves at a speed of \(60 \mathrm{~km} / \mathrm{h}\) through a magnetic field having a flux density of \(0.6 \mathrm{~T}\). Calculate the induced voltage.

Short Answer

Expert verified
The induced voltage in the moving conductor is 20 V.

Step by step solution

01

Convert the given speed to meters per second.

Given that the speed of the conductor is 60km/h, we need to convert this to meters per second, since the other units in the problem are in meters and seconds. To do this, we can simply multiply by 1000 to convert km to meters and then divide by 3600 to convert hours to seconds:\[Speed = \frac{60 \times 1000}{3600}=\frac{60000}{3600}= 16.67 \mathrm{\frac{m}{s}}\]
02

Calculate the magnetic force on the conductor.

Now, we need to calculate the magnetic force that acts on the conductor. To do this, we use the following formula: \[F = B \times l \times v\] where F is the induced force in Newtons (N), B is the magnetic flux density in Tesla (T), l is the length of the conductor in meters (m), and v is the velocity in meters per second (m/s). Using the given values, we get: \[F = 0.6 \mathrm{T} \times 2 \mathrm{m} \times 16.67 \mathrm{\frac{m}{s}} = 20 \mathrm{N}\]
03

Calculate the induced voltage.

Finally, we can find the induced voltage using Faraday's law of electromagnetic induction, which states: \[\epsilon = -\frac{d\Phi}{dt}\] Where 蔚 is the induced voltage in Volts (V), 桅 is the magnetic flux in Weber (Wb), and t is the time in seconds (s). In this case, the rate of change of magnetic flux with time can be expressed as: \[\frac{d\Phi}{dt} = Blv\] So, the induced voltage would be: \[\epsilon = - Blv = -(0.6 \mathrm{T} \times 2 \mathrm{m} \times 16.67 \mathrm{\frac{m}{s}}) = -20 \mathrm{V}\] (Note that the negative sign indicates that the induced voltage opposes the change in magnetic flux, as expected according to Lenz's law.)
04

Answer:

The induced voltage in the moving conductor is 20 V.

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