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Chapter 20: Q62P (page 861)

A metal rod of length L slides horizontally at constant speed v on frictionless insulating rails through a region of uniform upward magnetic field of magnitude B (Figure 20.124).

On a diagram, show the polarization of the rod and the direction of the Coulomb electric field inside the rod. Explain briefly. What is the magnitude of the Coulomb electric field inside the rod? What is the potential difference across the rod? What is the emf across the rod? What are the magnitude and direction of the force you have to apply to keep the rod moving at a constant speed v?

Short Answer

Expert verified

(i) E=BV

(ii)The diagram is drawn below.

(iii)e=BLV

(iv)F=B2L2VR

Step by step solution

01

Given Data

Length=LSpeed=v惭补驳苍别迟颈肠鈥凢颈别濒诲=B

02

Concept

The phenomenon occurred because of the wave nature of the radiation of the electromagnetic force is known as polarization.

03

Step 3(i): Find the magnitude of the Coulomb electric field inside the rod 

At equilibrium of electron inside the rod,

eE=eVBE=BV

Hence, the magnitude of the Coulomb electric field inside the rod E=BV

04

Step 4(ii): Find the potential difference across the rod

Since, electron experiences force in upward direction means 鈥渆lectric field鈥� is in downward direction .Therefore from A to B as shown in figure.

05

Step 5(iii): Find the emf across the rod

emf, (electric field= potential difference)

e=ELe=BLV

Hence, the emf across the rod ise=BLV

06

Step 6(iv): Find the force

Force,

F=BIL=BeRL=BBLVRLF=B2L2VR

Hence the force isF=B2L2VR

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Most popular questions from this chapter

We will consider the possibility that a free electron acted on by an electric field could gain enough energy to ionize an air molecule in a collision. (a) Consider an electron that starts from rest in a region where there is an electric field (due to some charged objects nearby) whose magnitude is nearly constant. If the electron travels a distance dand the magnitude of the electric field isE,what isthe potential difference through which the electron travels? (Pay attention to signs: Is the electron traveling with the electric field or opposite to the electric field?) (b) What is the change in potential energy of the system in this process? (c) What is the change in the kinetic energy of the electron in this process? (d) We found the mean free path of an electron in air to be about 5脳10-7鈥�m, and in the previous question you calculated the energy required to knock an electron out of an atom. What is the magnitude of the electric field that would be required in order for an electron to gain sufficient kinetic energy to ionize a nitrogen molecule? (e) The electric field required to cause a spark in air is observed to be about 3脳106鈥�V/mat STP. What is the ratio of the magnitude of the field you calculated in the previous part to the observed value at STP? (f) What is it reasonable to conclude about this model of how air becomes ionized? (1) Since we used accurate numbers, this is a huge discrepancy, and the model is wrong. (2) Considering the approximations we made, this is pretty good agreement, and the model may be correct.

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