A neutral metal rod of length 0.45 m slides horizontally at a constant speed of
ID: 2301888 • Letter: A
Question
A neutral metal rod of length 0.45 m slides horizontally at a constant speed of 7 m/s on frictionless insulating rails through a region of uniform magnetic field of magnitude 0.4 tesla, directed out of the page as shown in the diagram. Before answering the following questions, draw a diagram showing the polarization of the rod, and the direction of the Coulomb electric field inside the rod.
Which of the following statements is true?
The top of the moving rod is positive.The top of the moving rod is negative. The right side of the moving rod is positive.The right side of the moving rod is negative.The moving rod is not polarized.
To the leftTo the right No force is needed
Explanation / Answer
The top of the moving rod is positive.
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ZERO
Once the transient isover, the electrons would be displaced to the lower end of rod.These electrons will be pulled by electric force in upwardsdirection while the magnetic force will try to push them downwards.After the transient, they will balance each other and the net forcewill become zero.
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Electric fieldintensity |E| = V * B
= v * B * sin theta
= 7.0 * 0.5 * sin 900
= 3.5 N/C
Force onelectron F = e* E
= 1.6 * 10-19 * 3.5
= 5.6 * 10-19 N
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Magnetic forcemagnitude Fmag = v * e * B * sin theta
= 7.0 * 1.6 * 10-19 * 0.5 * sin 900
= 5.6 * 10-19 N
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InducedEMF deltaV = B * v * L * sin theta
= 0.5 * 7.0 * 0.45 * sin 90
= 1.575 V
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No force is needed
Since there is no force on rod ( friction) or Lorentz ( force of currentdue to magnetic field) no external force is required.
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