Chapter 30, Problem 1P

(a)

To determine

Whether the given statement is true or false.

Answer to Problem 1P

The given statement is False.

Explanation of Solution

Introduction:

Conduction current developed in conductors due to movement of electrons in it, while displacement current developed when atime-varying electric field sets upin a dielectric orcapacitor.

According to Maxwell's Ampere circuital Law, the line integral of magnetic field along a closed path is equal to ${\mu }_o$ times of the total current is given by,

  ${\displaystyle \oint B\cdot dl}={\mu }_o\text{}\left(i_c+i_d\text{}\right)$

Here, $i_c$ is conduction current and $i_d$ is displacement current.

So, both conduction current and displacement current have same unit.

Conclusion:

Thus, the given statement is False.

(b)

To determine

Whether the given statement is true or false.

Answer to Problem 1P

The given statement is True.

Explanation of Solution

Introduction:

Displacement current developed when atime-varying electric field sets upin a dielectric or capacitor. It was discovered by Maxwell.

According to Maxwell's the expression for displacement current $i_d$ is given by,

  $i_d={\epsilon }_o\frac{d{\varphi }_e}{dt}$

Here, ${\varphi }_e$ is the flux of the electric field.

So, when ${\varphi }_e$ is constant then $i_d$ is zero.

Hence, displacement current only exists if the electric field in the region changing with time.

Conclusion:

Therefore, the given statement is True.

(c)

To determine

Whether the given statement is true or false.

Answer to Problem 1P

The given statement is True.

Explanation of Solution

Introduction:

Displacement current developed when atime-varying electric field sets upin a dielectric or capacitor. It was discovered by Maxwell.

In an oscillating circuit, when the capacitor is momentarily fully charged the value of electric flux is maximum and constant. So, there is no displacement current.

Conclusion:

Therefore, the given statement is True.

(d)

To determine

Whether the given statement is true or false.

Answer to Problem 1P

The given statement is False.

Explanation of Solution

Introduction:

Displacement current developed when atime-varying electric field sets upin a dielectric or capacitor. It was discovered by Maxwell.

In an oscillating $LC$ circuit, when the capacitor is momentarily uncharged the rate of change of electric field is given by,

  $\frac{dE}{dt}\ne 0$

So, rate of change of electric flux is given by,

  $\frac{d{\varphi }_e}{dt}\ne 0$

Hence, displacement current is given by,

  $\begin{array}{c}{i}_d={\epsilon }_o\frac{d{\varphi }_e}{dt}\\ i_d\ne 0\end{array}$

Conclusion:

Therefore, the given statement is False.