MCQ
A parallel plate capacitor has a parallel sheet of copper inserted between and parallel to the two plates, without touching the plates. The capacity of the capacitor after the introduction of the copper sheet is :
  • A
    minimum when the copper sheet touches one of the plates.
  • B
    greater than that before introducing the sheet.
  • C
    invariant for all positions of the sheet between the plates.
  • $B$ and $C$ both

Answer

Correct option: D.
$B$ and $C$ both
d
As the copper is a good conductor, the charge on the capacitor will appear on the large flat surfaces of the copper sheet, with the negative side of the copper facing the positive side of the capacitor. This arrangement can be considered to be two capacitors in series.

If thickness of the copper slab is $l$, the separation of plates between will be $\frac{1}{2}(d-l)$ The capacitance before insert slab is $C=\frac{A \in_{0}}{d}$

The capacitance of each capacitor after insert slab is $C^{\prime}=\frac{A \in_{0}}{(d-l) / 2}$

Net capacitance after insert slab is $C_{e q}=\frac{C^{\prime} C^{\prime}}{C^{\prime}+C^{\prime}}=\frac{c^{\prime}}{2}=\frac{A \in_{0}}{(d-l)}$

thus, $C_{e q}>C$ and if sheet is very thin $(d>>l), C_{e q}=C$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

In figure two parallel infinitely long current carrying wires are shown. If resultant magnetic field at point $A$ is zero. Then determine current $I.$ (in $A$)
What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of $150 \,{km}$ ? The average population density around the tower is $2000 \,/ {km}^{2}$ and the value of ${R}_{{e}}=6.5 \times 10\, {m}$
In an electromagnetic wave, the amplitude of electric field is $1 V/m.$  the frequency of wave is $5 \times {10^{14}}\,Hz$. The wave is propagating along $z-$ axis. The average energy density of electric field, in $Joule/m^3$, will be
Consider the inferences given below in respect of the following current loop of wire kept is a magnetic field $\vec B$

$A.$ The force on the element $AC$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$B.$ The force on the element $AB$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$C.$ The total force on the loop $ABCA$ is zero.

Which of the above is /are not true ?

A capacitor is fully charged with a battery. Then the battery is removed and coil is connected with the capacitor in parallel, current varies as
For the given input voltage waveform $V_{\text {in }}( t )$, the output voltage waveform $V _{ D }( t ),$ across the capacitor is correctly depicted by:
The magnetic field at the center of current carrying circular loop is $B _{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_{2}$. The value of $B_{1} / B_{2}$ will be.
A current of $5$ $ampere$ is flowing in a wire of length $1.5$ $metres$. A force of $7.5\, N$ acts on it when it is placed in a uniform magnetic field of $2\, Tesla$. The angle between the magnetic field and the direction of the current is......$^o$
The equation $E = pc$ is valid:
The thermionic emission of electron is due to