7

If there are charges left in any of the terminals, why approaching one terminal from a piece of paper or an electroscope doesn't show any kind of static electricity ? It is simply a matter of scale. A battery would have 1.5 V to 12 V worth of static electricity, but the minimum detection threshold for a human is about 3 kV of static electricity. So there is ...


4

Both earthed points are different (physically). I want to learn how this capacitor is getting charged The fact that the power supply and one plate of the capacitor are earth grounded at different locations simply potentially introduces additional resistance through which charging occurs. That resistance increases the charging time constant (t=RC) slowing ...


3

In Figure V.16 the equipotential surfaces between the two plates are all parallel to the plates. So the line (surfaces) labelled $V$ is an equipotential. Putting in an infinitesimally thin sheet of conductor along that equipotential surface makes no difference to the electrical properties of the capacitor. Now increasing the thickness of the conductor again ...


1

Is $L$ along the $z$-direction? Not that is matters. Since the correct answer goes as $1/L^2$, you are looking a pure monopole field (or the cylindrical field equivalent). A monopole field is radially outward with magnitude: $$ E = k\frac q{r^2},$$ where $q$ is the total charge. It suffices to show that: $$ q=\int\sigma(r,\phi)dr d\phi = \frac 1 3 \sigma_0 \...


1

I think you are being confused with charge and net charge. An uncharge sphere does have positive and negative charges, the only thing is that the magnitudes of positive and negative charges are equal and so there is no net charge. Another way to think is that there are both electrons and protons in a metallic sphere right? Arent they both charged?


1

The electrons in fur are much less tightly bound than electrons in ebonite (very strong relative bond, ebonite is at the bottom of the negative Triboelectric series, see [1]) and hence ebonite gets a strong relative negative charge [1]. "A material towards the bottom of the Triboelectric series table, when touched to a material near the top of the ...


1

There are a few issues to unpack here. First, note that what you have defined is not really the charge density. Let's write out this quantity explicitly: \begin{equation} \hat{\rho}(x',y',z', \theta) = \lambda \delta(x'-x(\theta)) \delta(y'-y(\theta)) \delta(z'-z(\theta)), \end{equation} Note that I have defined $\hat\rho$ with an explicit dependence on $\...


1

Instead of a cube, use an infinite slab (so the transverse coordinates don't matter). We have: $$ E(x) = E_0 $$ Then $\nabla \vec E \rightarrow dE/dx$, so with no conductor: $$ \frac{dE}{dx} = \frac 1 {\epsilon_0}\rho(x)= 0$$ which of course is solved by $E(x)=E_0$. Now place a conductor with a surface at $x=0$. A charge is induced: $$ \rho(x) = E_0 \...


1

As long as the hollow conductor has thickness, the total amount of charge $+q$ on the outer surface migrates to the inner surface after $-q$ has been inserted in the cavity. That'll be still consistent with the Gauss' Law.


1

The external force is the negative of the field force. f.dr is work done by the field, -f.dr is the work done against


1

The electrons in fur are much less tightly bound than electrons in ebonite (very strong relative bond, ebonite is at the bottom of the negative Triboelectric series, see [1]) and hence ebonite gets a strong relative negative charge [1]. "A material towards the bottom of the Triboelectric series table, when touched to a material near the top of the ...


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