# Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint Consider how drift velocity depends on wire diameter.)

### College Physics

1st Edition
Paul Peter Urone + 1 other
Publisher: OpenStax College
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
Publisher: OpenStax College
ISBN: 9781938168000
Chapter 22, Problem 29PE
Textbook Problem
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## Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint Consider how drift velocity depends on wire diameter.)

To determine

Show that the Hall voltage induced is inversely proportional to the wire diameter.

### Explanation of Solution

The hall voltage induced is given by the formula

ε=vBl ...... (1)

Here,

v is the electron velocity

B is the magnetic field

l is the length of the conductor

Now the drift velocity of the electron is given by the formula

v=InqA

Here,

n is the number of electrons per unit volume

q is the charge of the electron

A is the area

Rearranging the formula of drift velocity in terms of diameter

v=In

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