Chapter 27: Q. 3 (page 762)

$1.0 \times 10^{16}$ electrons flow through a cross section of a silver wire in $320 μ s$ with a drift speed of $8.0 \times 10^{- 4} m / s$ . What is the diameter of the wire?

Short Answer

Expert verified

The diameter of the wire is $0.93 m m$ .

Step by step solution

Given Information

Number of electrons $= 1.0 \times 10^{16}$

Time $= 320 μ s$

Drift speed $= 8.0 \times 10^{- 4} m / s$

Explanation

The electron density is

$i_{e} : = \frac{N}{t}$

The current density is known to be

$i_{e} = n_{e} A v_{d} .$

The area of a circle is,

$A = \frac{π D^{2}}{4} \Rightarrow D = \sqrt{\frac{4 A}{π}} .$

Write the area as

$A = \frac{i_{e}}{n_{e} v_{d}}$

Write the electron current and substitute,

$A = \frac{N}{n_{e} t v_{d}}$

Now, substituting this expression for the area at the one for the diameter,

$D = \sqrt{\frac{4 N}{π n_{e} t v_{d}}} .$

After substituting the values,

localid="1649322696741" $D = \sqrt{(\frac{4 \times 1 \times 10^{16} e}{π \times 5.8 \times 10^{28} e \times 3.2 \times 10^{- 4} μ s \times 8 \times 10^{- 4} m / s})}$

localid="1649322704585" $= 9.26 \times 10^{- 4} m .$

Final Answer

Hence, the diameter of the wire is $9.26 \times 10^{- 4} m .$

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Voltage (V)	Current (A)
0.200	0.47
0.400	1.06
0.600	1.53
0.800	1.97

$1.0 \times 10^{16}$ electrons flow through a cross section of a silver wire in $320 μ s$ with a drift speed of $8.0 \times 10^{- 4} m / s$ . What is the diameter of the wire?

Short Answer

Step by step solution

Given Information

Explanation

Final Answer

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1.0×1016electrons flow through a cross section of a silver wire in 320μs with a drift speed of 8.0×10-4m/s. What is the diameter of the wire?

Short Answer

Step by step solution

Given Information

Explanation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Space Physics

Torque and Rotational Motion

Physical Quantities And Units

Fields in Physics

Oscillations

Study anywhere. Anytime. Across all devices.

$1.0 \times 10^{16}$ electrons flow through a cross section of a silver wire in $320 μ s$ with a drift speed of $8.0 \times 10^{- 4} m / s$ . What is the diameter of the wire?