Displacement Vector

Q.

What happens to the energy stored in a capacitor if the separation between the plates is doubled after it is disconnected form the battery?

Q.

How will the capacitance change if we increase the distance between the two plates?

Q. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor.

Q.

Two capacitors when connected in series have a capacitance of $3\mathrm{\mu F}$, and when connected in parallel have a capacitance of $16\mathrm{\mu F}$. Their individual capacities are :

1. 1μF, 2 μF

2. 6 μF, 2 μF

3. 12 μF, 4 μF

4. 3 μF, 6 μF

Q.

Let $C_1$ be the curve obtained by the solution of the differential equation $2xy\left(\frac{dy}{dx}\right)=y^2-x^2$, $x>0$. Let curve$C_2$ be the solution of $\frac{2xy}{x^2-y^2}=\frac{dy}{dx}$. If both the curves pass through $\left(1,1\right)$, then the area enclosed by the curves $C_1$ and $C_2$ is equal to:

1. $\frac{\mathrm{\pi }}{2}-1$

2. $\frac{\mathrm{\pi }}{4}+1$

3. $\mathrm{\pi }-1$

4. $\mathrm{\pi }+1$

Q. If the surface area of each surface of a plate is $A$ and separation between two adjacent plates is $d$. Calculate the charge given by the battery.

1. $\frac{2}{3}\left(\frac{{\epsilon }_{0}A}{d}\right)V_0$
2. $\frac{3{\epsilon }_{0}A}{d}{V}_0$
3. $\frac{{\epsilon }_{0}A}{d}{V}_0$
4. $\frac{1}{4}\frac{{\epsilon }_{0}A}{d}{V}_0$

Q. A charged parallel plate capacitor has an energy $U$ in the system. A slab of dielectric constant $K$ is inserted, which completely fills the space between the plates. The new energy of the system will be

1. $KU$
2. $K^{2}U$
3. $U/K$
4. $U/K^2$

Q. A parallel-plate capacitor is located horizontally so that one of its plates is submerged into a liquid while the other is over its surface. The permittivity of the liquid is equal to $ϵ$. Its density is equal to $\rho$. To what height will the level of the liquid in the capacitor rise after its plate get a charge of surface density $\sigma$ ?

1. No change in liquid level
2. $\frac{{\rho }^2({\in }^2-1)}{{\in }_0\rho g}$
3. $\frac{{\rho }^2({\in }^2-1)}{2{\in }_0\rho g{\in }^2}$
4. $\frac{{\rho }^2(\in -1)}{{\in }_0\rho g}$

Q. Why does current in a steady state not flow in a capacitor connected across a battery but a momentary current does flow during charging or discharging of the capacitor?

Q. The energy and capacity of a charged parallel plate capacitor are $E$ and $C$ respectively. Now a dielectric slab of ${ϵ}_r=6$ is inserted in it, then energy and capacity becomes
(Assuming charge on plates remains constant)

1. $6E,6C$
2. $E,C$
3. $\frac{E}{6},6C$
4. $E,6C$

Q.

what is the dimensional formula of potential gradient?

Q. Two thin parallel threads carry a uniform charge with linear densities λ and —λ. The distance between the threads is equal to l. Find the potential of the electric field and the magnitude of its strength vector at the distance r >> l at the angle θ to the vector l .

Q. Assertion: Displacement current goes to the gap between the plates of a capacitor when the charge of the capacitor does not change Reason: the displacement current arises in the region in which the electric field does not change with time

Q. Five similar condenser plates, each of area $A$ are placed at equal distance $d$ apart and are connected to source voltage $V$ as shown in the following diagram. The charge on plates $1$ and $4$ will be:

1. $\frac{{ϵ}_{o}A}{d},\frac{-2{ϵ}_{o}A}{d}$
2. $\frac{{ϵ}_{o}AV}{d},\frac{-2{ϵ}_{o}AV}{d}$
3. $\frac{-{ϵ}_{o}AV}{d},\frac{-3{ϵ}_{o}AV}{d}$
4. $\frac{{ϵ}_{o}AV}{d},\frac{-4{ϵ}_{o}AV}{d}$

Q.

How fast can a capacitor charge?

Q. Figure 8.6 shows a capacitor made of two circular plates each ofradius 12 cm, and separated by 5.0 cm. The capacitor is beingcharged by an external source (not shown in the figure). Thecharging current is constant and equal to 0.15A. (a) Calculate the capacitance and the rate of change of potentialdifference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of thecapacitor? Explain.

Q. a 3 microF capacitor is charged to a potential of 100V and 2microF capacitor is charged to 100V . the capacitors are then connected in parallel with plates of opposite polarities joined together. the amount of charge flown is ?

Q. The net capacitance of the system shown in the figure is -

1. $\frac{25}{24}\frac{{ϵ}_0\text{A}}{d}$
2. $\frac{24}{25}\frac{{ϵ}_0\text{A}}{d}$
3. $\frac{21}{10}\frac{{ϵ}_0\text{A}}{d}$
4. $\frac{10}{21}\frac{{ϵ}_0\text{A}}{d}$

Q. Assertion: Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor does not change.
Reason: The displacement current arises in the region in which the electric field and hence the electric flux Goes not change with time.

1. If both assertion and reason are true but the reason is the correct explanation of assertion.
2. If both assertion and reason are true but the reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both the assertion and reason are false.
5. If reason is true but assertion is false.

Q. In a medium of dielectric constant $K$, the electric field is $\overrightarrow{E}$. If ${ϵ}_0$ is permittivity of the free space, the electric displacement vector is :

1. $\frac{K\overrightarrow{E}}{{ϵ}_0}$
2. ${Kϵ}_0\overrightarrow{E}$
3. $\frac{{ϵ}_0\overrightarrow{E}}{K}$
4. $\frac{\overrightarrow{E}}{{Kϵ}_0}$

Q. Find the capacitance between the plates shown in the figure below

1. $\frac{{\in }_0{K}_1{K}_{2}bl}{d(K_2-K_1)}ln\frac{K_2}{K_1}$
2. $\frac{{\in }_0{K}_1{K}_{2}bl}{2d(K_2-K_1)}ln\frac{K_2}{K_1}$
3. $\frac{{\in }_0{K}_1{K}_{2}bl}{3d(K_2-K_1)}ln\frac{K_2}{K_1}$
4. None of the above

Q. An electric displacement vector can be defined as a vector sum of fields due to polarization and the electric field vector.

1. False
2. True

Q. Across a metallic conductor of non uniform cross section a cons†an t potential difference is applied. The quantity which remains cons†an t along the conductor

Q. the dimensions of 1/2 e^0 E^x , where e^ is permittivity of free space and E is electric field is

Q. what is the relation between electric field intensity and electric potential?

Q. A parallel plate capacitor of capacitance $90pF$ is connected to a battery of emf $20V$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be

1. $2.4nC$
2. $0.9nC$
3. $1.2nC$
4. $0.3nC$

Q. A capacitor of capacitance 3 micro farad is connected with an EMF 3 volt electrostatic energy stored in the capacitor is

Q. An isolated capacitor with a capacitance C has a potential difference between the plates of V, which leaves on each plate a charge $Q$.
A dielectric is then inserted in-between the plates, what affect does this have on the electric field between the plates?

1. The electric field increases in magnitude.
2. The electric field decreases in magnitude.
3. The direction of the electric field changes as well as the magnitude.
4. The electric field magnitude is not affected.

Q.

How does dielectric decrease electric field?

Q. A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at $x=0$ and positive plate is at $x=3d$. The slab is equidistant from the pates. The capacitor is given some charge. As one goes from 0 to 3d :

1. the magnitude of the electric field remains the same
2. the direction of the electric field remains the same
3. the electric potential increases at first, then decreases and again increases
4. the electric potential decreases continuously