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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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