Chapter 31: Q. 36 (page 902)

A wire with conductivity s carries current $I$ . The current is increasing at the rate $d I / d t .$
a. Show that there is a displacement current in the wire equal to $(\in o / σ_{}) (d I / d t)$
b. Evaluate the displacement current for a copper wire in which the current is increasing at $1.0 \times 10^{6} A / s .$

Short Answer

Expert verified

a) The displacement current in the wire is equal to $I_{d} = \in o {\frac{d \emptyset e_{}}{d t}}_{}$

b) The displacement current in wire in which current is increasing at $1.0 \times 10^{6} A / s$ is $I_{d} = 1.48 \times 10^{- 13} A$ .

Step by step solution

Part(a) Step1: Given information

We have given that In the wire the current density $\underset{J}{\to}$ is related to the electric field localid="1649944213928" $\underset{J}{\to} = σ \underset{E}{\to}$ , Integrating over a cross section of the wire , we have $I = σ ϕ_{E}$ ,

so $ϕ_{E} = \frac{I}{σ}$

$\frac{d ϕ_{E}}{d t} = \frac{1}{σ} \frac{d I}{d t}$

Part(a) Step2: Simplify

The displacement of current $I_{d}$ is:

$I_{d} = \in o_{} \frac{d ϕ_{e}}{d t}$

$I_{d} = {\frac{\in o_{}}{σ}}_{} \frac{d I}{d t}$ ${ϕ_{E} = \frac{I}{σ}}$

Part(b) Step1: Given information

We have given that For copper, the vacuum permittivity is $\in o = 8.85 \times 10^{- 12} {\frac{F}{m}}_{}$ and $σ = 5.95 \times 10^{7} \frac{S}{m}$

we calculate values for $I_{d}$ ;

Part(b) Step2: Explanation

$I_{d} = {\frac{\in o_{}}{σ}}_{} \frac{d I}{d t}$

$I_{d} = \frac{8.85 \times 10^{- 12}}{5.95 \times 10^{7}} 1.0 \times 10^{6}$

$I_{d} = 1.45 \times 10^{- 13} A_{}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Part(a) Step1: Given information

Part(a) Step2: Simplify

Part(b) Step1: Given information

Part(b) Step2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Electricity

Atoms and Radioactivity

Dynamics

Classical Mechanics

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

A wire with conductivity s carries current I. The current is increasing at the rate dI/dt.a. Show that there is a displacement current in the wire equal to (∈o/σ)(dI/dt)b. Evaluate the displacement current for a copper wire in which the current is increasing at 1.0×106A/s.

Short Answer

Step by step solution

Part(a) Step1: Given information

Part(a) Step2: Simplify

Part(b) Step1: Given information

Part(b) Step2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Electricity

Atoms and Radioactivity

Dynamics

Classical Mechanics

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.