Electromagnetism and Charge Conservation Flashcards (37 cards)

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1Question

What is Maxwell-Gauss’ local equation?

Answer

$\operatorname{div}(\vec E)=\frac{\rho(M,t)}{\varepsilon_0}$

2Question

What is Maxwell-Faraday’s local equation?

Answer

$\operatorname{rot}(\vec E)=-\frac{\partial \vec B}{\partial t}$

3Question

What is the local magnetic-flux equation?

Answer

$\operatorname{div}(\vec B)=0$

4Question

What is Maxwell-Ampère’s local equation?

Answer

$\operatorname{rot}(\vec B)=\mu_0\vec j+\mu_0\varepsilon_0\frac{\partial \vec E}{\partial t}$

5Question

What does surface charge density measure?

Answer

Charge per area.

6Question

What does linear charge density measure?

Answer

Charge per length.

7Question

What is the current density for one charge-carrier type at point $P$ ?

Answer

$\vec j_1(P)=n_{1m}q_{1m}\vec v_1(P)$

8Question

How is current from one carrier type calculated through surface $S$ ?

Answer

$i_{S1}=\iint_{P\in(S)}\vec j_1(P)\cdot d\vec S$

9Question

How is total current through surface $S$ calculated from current density?

Answer

$i_{(S)}=\iint_{P\in(S)}\vec j(P)\cdot d\vec S(P)$

10Question

What is the one-dimensional local charge conservation equation?

Answer

$\frac{\partial\rho}{\partial t}+\frac{\partial j}{\partial x}=0$

11Question

What is the three-dimensional local charge conservation equation?

Answer

$\frac{\partial\rho}{\partial t}+\operatorname{div}(\vec j)=0$

12Question

In a stationary regime, what is the time derivative of charge density?

Answer

$\frac{\partial\rho}{\partial t}=0$

13Question

In a stationary regime, what is the divergence of current density?

Answer

$\operatorname{div}(\vec j)=0$

14Question

What is the total current through any closed surface in a stationary regime?

Answer

Zero.

15Question

What is the integral Gauss law for electric flux through a closed surface?

Answer

$\oiint_{P\in(S)}\vec E(P)\cdot d\vec S(P)=\frac{Q_{\mathrm{int}}(V)}{\varepsilon_0}$

16Question

What is the generalized integral Ampère law?

Answer

$\oint_{P\in(C)}\vec B(P,t)\cdot d\vec\ell(P)=\mu_0 I(S)+\mu_0\varepsilon_0\iint_{M\in(S)}\frac{\partial\vec E}{\partial t}\cdot d\vec S(M)$

17Question

What integral defines magnetic flux through a surface?

Answer

$\Phi=\iint_{M\in(S)}\vec B(M,t)\cdot d\vec S(M)$

18Question

What is Maxwell–Faraday’s integral law for an immobile surface?

Answer

$\oint_{P\in(C)}\vec E(P,t)\cdot d\vec\ell(P)=-\frac{d\Phi}{dt}$

19Question

How is electromotive force defined in terms of magnetic flux?

Answer

$e=-\frac{d\Phi}{dt}$

20Question

How are the vacuum constants related to the speed of electromagnetic waves?

Answer

$\mu_0\varepsilon_0=\frac{1}{c^2}$

21Question

In the vacuum-constant relation, what does $c$ represent?

Answer

The speed of electromagnetic waves in vacuum.

22Question

How is total charge on a surface distribution calculated?

Answer

$Q_S=\iint_{M\in(S)}\sigma(M)\,dS$

23Question

Where is the electric field undefined in the described distributions?

Answer

Under the surface and line charge distributions.

24Question

What is the total current density for multiple carrier types at point $P$ ?

Answer

$\vec j=\sum_k n_{km}q_{km}\vec v_k(P)$

25Question

In what units is current density $\vec j$ measured?

Answer

$\mathrm{A\cdot m^{-2}}$

26Question

How is charge inside a fixed volume defined?

Answer

$Q_{(V)}(t)=\iiint_{M\in(V)}\rho(M,t)\,d\tau(M)$

27Question

How is current crossing a closed surface defined?

Answer

$i_S(t)=\oiint_{P\in(S)}\vec j(P,t)\cdot d\vec S(P)$

28Question

What happens when current density points along an outward surface element?

Answer

Charge leaves the volume, so the volume loses charge.

29Question

At a stationary junction, what equation relates the signed currents?

Answer

$I_1+I_2+I_3=0$

30Question

For a current-density tube with no lateral current, how do its end currents compare?

Answer

$I_1=I_2$

31Question

What role do electric charges play in relation to the electric field?

Answer

They are sources of the electric field.

32Question

What is Ampère’s law in a stationary regime?

Answer

$\oint_{P\in(C)}\vec B(P,t)\cdot d\vec\ell(P)=\mu_0 I$

33Question

How is the contour direction in the Ampère integral determined?

Answer

By the right-hand rule relative to the oriented surface.

34Question

What is the net magnetic flux through a closed surface?

Answer

Zero.

35Question

What are the four coupled equations in $\vec E$ and $\vec B$ useful for describing?

Answer

Electromagnetic waves.

36Question

What is the electric-field relation across the charged surface?

Answer

$\vec E(P_1)-\vec E(P_2)=\frac{\sigma}{\varepsilon_0}$

37Question

What is the approximate vacuum electric permittivity?

Answer

$8.85\times10^{-12}\ \mathrm{F\cdot m^{-1}}$

Test yourself with the quiz

Answer 12 questions on Electromagnetism and Charge Conservation.

1. A field measurement gives $\operatorname{div}(\vec E)=\frac{\rho(M,t)}{\varepsilon_0}$ and a time-varying magnetic field. Which statements correctly identify the local electric-field equations?

2. In a region, the electric field changes with time and a current density is present. Which statements correctly describe the local magnetic-field equations?

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Electromagnetism and Charge Conservation Flashcards (37 cards)

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