Question

Discharging Capacitor A capacitor with square plates of edge length $L$ is being discharged by a current of $0.75$ A. Figure $31-49$ is a Fic head-on view of one of the plates Pro from inside the capacitor. A dashed rectangular path is shown. If $L=12 \mathrm{~cm}$, $W=4.0 \mathrm{~cm}$, and $H=2.0 \mathrm{~cm}$, what is the value of $\{\vec{B} \cdot d \vec{s}$ around the dashed path?

Name: Problem 45, Chapter 31: Understanding Physics
Uploaded: 2021-12-07T11:41:17-08:00
Duration: 1 min 48 s
Channel: Amit Srivastava
Description: Discharging Capacitor A capacitor with square plates of edge length L is being discharged by a current of 0.75 A. Figure 31-49 is a Fic head-on view of one of the plates Pro from inside the capacitor. A dashed rectangular path is shown. If L=12 cm, W=4.0 cm, and H=2.0 cm, what is the value of {B⃗ ·d s⃗ around the dashed path?

   Discharging Capacitor A capacitor with square plates of edge length $L$ is being discharged by a current of $0.75$ A. Figure $31-49$ is a Fic head-on view of one of the plates Pro from inside the capacitor. A dashed rectangular path is shown. If $L=12 \mathrm{~cm}$, $W=4.0 \mathrm{~cm}$, and $H=2.0 \mathrm{~cm}$, what is the value of $\{\vec{B} \cdot d \vec{s}$ around the dashed path?

Understanding Physics

Karen Cummings,… 1st Edition

Chapter 31, Problem 45

Instant Answer

Solved by Expert Amit Srivastava

12/07/2021

Step 1

75$ A. We are also given a head-on view of one of the plates from inside the capacitor with a shaded rectangular path of height $H$ and width $W$. The given data is $L=12$ cm, $W=4.0$ cm, and $H=2.0$ cm. We are asked to find the value of $\int \vec{B} \cdot Show more…

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Discharging Capacitor A capacitor with square plates of edge length $L$ is being discharged by a current of $0.75$ A. Figure $31-49$ is a Fic head-on view of one of the plates Pro from inside the capacitor. A dashed rectangular path is shown. If $L=12 \mathrm{~cm}$, $W=4.0 \mathrm{~cm}$, and $H=2.0 \mathrm{~cm}$, what is the value of $\{\vec{B} \cdot d \vec{s}$ around the dashed path?

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Key Concepts

Ampere's Circuital Law (with Maxwell’s Correction)

Ampere's Law, in its extended form which includes Maxwell's correction, establishes that the closed line integral of the magnetic field around any loop is proportional to the sum of the conduction current and the displacement current (which accounts for the time-varying electric field) passing through the surface bounded by the loop. This principle is essential for analyzing magnetic fields in circuits where the electric field is not static, such as within a charging or discharging capacitor.

Displacement Current

The displacement current is an effective current term introduced by Maxwell to account for the changing electric flux in regions where there is no actual motion of charge, such as between the plates of a capacitor. It ensures the continuity of current in circuits involving time-varying fields, allowing Ampere's Law to be applied universally even in gaps where conventional conduction current does not exist.

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