Chapter 4: Q4E (page 842)

An 18-gauge copper wire (diameter 1.02 mm) carries a current
with a current density of $3.2 \times 10^{6} \frac{A}{m^{2}}$ . The density of free electrons for
copper is $8.5 \times 10^{28}$ electrons per cubic meter. Calculate (a) the current in
the wire and (b) the drift velocity of electrons in the wire.

Short Answer

Expert verified

a) The current in the wire is $/ = 2.61 A$ .

b) The drift velocity of the electrons in the wire is $V_{d} = 2.353 \times 10^{- 4} \frac{m}{s}$

Step by step solution

Formula of current and velocity drift.

Consider the area of cross section is

$A = \frac{{πd}^{2}}{4}$

Here, dis the diameter.

Consider the expression for the current is:

$V_{d} = \frac{J}{nq \frac{{πd}^{2}}{4}}$ ….. (1)

Here, nis the charge concentration and q is the charge.

Consider the expression for the current density:

$J = \frac{I}{A} I = JA$

Rewrite as:

$I = J \frac{{πd}^{2}}{4}$ …… (2)

Determine the value for the current.

(a)

Given is the density of current in the wire as $3.2 \times 10^{6} \frac{A}{m^{2}}$

Diameter of the wire as $1.02 \times 10^{- 3} m$

Substitute the values in the equation (2) and solve as,

$I = (3.2 \times 10^{6} \frac{A}{m^{2}}) (\frac{π {(1.02 \times 10^{- 3} m)}^{2}}{4}) = 2.61 A$

Calculation of velocity drift.

(b)

Given the number of electrons as $8.5 \times 10^{28}$ and the charge of a electron is

$1.6 \times 10^{- 19}$ coulombs.

Substitute the values in the equation (1) and solve as,

$V_{d} = \frac{(3.2 \times 10^{6} \frac{A}{m^{2}})}{8.5 \times 10^{28} \times 1.6 \times 10^{- 19}} = 2.353 \times 10^{- 4} \frac{m}{s}$

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Short Answer

Step by step solution

Formula of current and velocity drift.

Determine the value for the current.

Calculation of velocity drift.

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An 18-gauge copper wire (diameter 1.02 mm) carries a currentwith a current density of 3.2×106Am2. The density of free electrons forcopper is8.5×1028electrons per cubic meter. Calculate (a) the current inthe wire and (b) the drift velocity of electrons in the wire.

Short Answer

Step by step solution

Formula of current and velocity drift.

Determine the value for the current.

Calculation of velocity drift.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Circular Motion and Gravitation

Mechanics and Materials

Turning Points in Physics

Energy Physics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.