Question

In a particular metal, the mobility of the mobile electrons is . At a particular moment the net electric field everywhere inside a cube of this metal isin thedirection. What is the average drift speed of the mobile electrons in the metal at this instant?

Short answer

The average drift speed of the mobile electrons in the metal is $4.08\times {10}^{-4}$m/s.

Step-by-step solution

Identification of given values

The given data is listed below as:

• The value of the net electric field of the metal is,$E=0.053\mathrm{N}/\mathrm{C}$
• The mobile electron’s mobility is,$u=0.0077\mathrm{m}/\mathrm{s}/\mathrm{N}/\mathrm{C}$

Significance of the average drift

The speed at which mobile charges move through a conductor is called the drift speed. Moreover, the average drift is calculated as the product of the value of the net electric field and the mobile electron’s mobility.

Calculation of the average drift speed

The equation of the average drift speed of the mobile electrons is expressed as:

$v=uE$

Here, $u$is the mobile electron’s mobility and $E$is the value of the net electric field.

Substitute the values in the above equation.

role="math" localid="1656925397222" $v=0.0077\mathrm{m}/\mathrm{s}/\mathrm{N}/\mathrm{C}\times 0.053\mathrm{N}/\mathrm{C}$

role="math" localid="1656925368417" $=4.08\times {10}^{-4}\mathrm{m}/\mathrm{s}$

Thus, the average drift speed of the mobile electrons in the metal is role="math" localid="1656925344278" $4.08\times {10}^{-4}\mathrm{m}/\mathrm{s}$.