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Chapter 20: Q4Q (page 852)

A copper wire with square cross section carries a conventional current I to the left (as in Figure 20.83). There is a magnetic field B perpendicular to the wire. Describe the direction of E鈯�, the transverse electric field inside the wire due to the Hall effect, and explain briefly.

Short Answer

Expert verified

The Hall electric fieldE鈯� is directed into the paper which opposes the magnetic force on the flowing electrons in the wire.

Step by step solution

01

Given data

Conventional current in the wire isI .

Magnetic field in the region isB .

02

Magnetic force

Magnetic force on a moving charge is the product of the magnitude of the charge and the cross product of the velocity vector and the magnetic field.

03

Determination of the direction of the Hall electric field

The copper wire contains moving electrons which experience a magnetic force in the presence of a magnetic field. The conventional current is flowing to the left and thus the electrons are flowing to the right. The force on them is directed into the paper. The negative charges accumulate into the far end of the wire. This creates a perpendicular electric field E鈯� directed into the paper that prevents further flow of electrons towards the far side due to the magnetic force. This is known as the Hall field.

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Most popular questions from this chapter

A neutral metal rod of length 60 cm falls toward the Earth. The rod is horizontal and oriented east west. (1) Which end of the rod, east or west, has excess electrons? Explain using physics diagrams. (2) At a moment when the rod鈥檚 speed is 4m/s , approximately how many excess electrons are at the negative end of the rod?

Explain briefly why there is a limit to how much charge can be placed on a metal sphere in the classroom. If the radius of the sphere is 15鈥�cm what is the maximum amount of charge you can place on the sphere? (Remember that a uniform sphere of charge makes an electric field outside the sphere as though all the charge were concentrated at the center of the sphere.)

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?

An electron is moving with a speed v in the plane of the page (Figure 20.81), and there is a uniform magnetic field Binto the page throughout this region; the magnetic field is produced by some large coils that are not shown. Draw the trajectory of the electron, and explain qualitatively.

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