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A charge –q is placed at the axis of a charged ring of radius r at a distance of $2\sqrt{2} \mathrm{r}$  as shown in figure. If ring is fixed and carrying a charge Q, the kinetic energy of charge –q when it is released and reaches the centre of ring will be,

1. $\frac{\mathrm{qQ}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$
2. $\frac{\mathrm{qQ}}{12{\mathrm{\pi \epsilon }}_0\mathrm{r}}$
3. $\frac{\mathrm{qQ}}{6{\mathrm{\pi \epsilon }}_0\mathrm{r}}$
4. $\frac{\mathrm{qQ}}{2{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

Figure shown in five capacitors connected across a 12 V power supply. What is the potential drop across the 2$\mathrm{\mu }$F capacitor?

1. 2 V 
2. 4 V
3. 8 V 
4. 10 V

A parallel plate capacitor is maintained at a certain potential difference. When a dielectric slab of thickness 3 mm is introduced between the plates, the plate separation had to be increased by 2 mm in order to maintain the same potential difference between the plates. The dielectric constant of the slab is
1. 2 
2. 3 
3. 4 
4. 5

A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be $\frac{1}{4{\mathrm{\pi \epsilon }}_0}$ times (potential at infinity is zero)
1. $\frac{\mathrm{q}}{2\mathrm{R}}$
2. $\frac{4\mathrm{q}}{3\mathrm{R}}$
3. $\frac{5\mathrm{q}}{3\mathrm{R}}$
4. $\frac{2\mathrm{q}}{3\mathrm{R}}$

Two conducting plates X and Y, each having large surface area A (on one side) are placed parallel to each other. The plate X is given a charge Q whereas the other is neutral. The electric field at a point in between the plates is given by

1. $\frac{\mathrm{Q}}{2\mathrm{A}}$
2. $\frac{\mathrm{Q}}{2{\mathrm{A\epsilon }}_0}$ towards left
3. $\frac{\mathrm{Q}}{2{\mathrm{A\epsilon }}_0}$ towards right
4. $\frac{\mathrm{Q}}{2{\mathrm{\epsilon }}_0}$ towards right

A solid hemispherical uniform charged body having charge Q is kept symmetrically along the y-axis as shown in figure. The electric potential at a distance d from the origin along the x-axis at point P will be

1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q}{d}$
2. less than $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q}{d}$
3. more than $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q}{d}$ and less than $\frac{2}{4{\mathrm{\pi \epsilon }}_0}\frac{Q}{d}$
4. more than $\frac{2}{4{\mathrm{\pi \epsilon }}_0}\frac{Q}{d}$

In the given circuit the value of charge across capacitor AB as a function of time is 

1. $\mathrm{CE}\left(1-{\mathrm{e}}^{-\frac{\mathrm{t}}{2\mathrm{RC}}}\right)$
2. $2\mathrm{CE}\left(1-{\mathrm{e}}^{-\frac{\mathrm{t}}{2\mathrm{RC}}}\right)$
3. $\mathrm{CE}/2\left(1-{\mathrm{e}}^{-\frac{-2t}{\mathrm{RC}}}\right)$
4. $2\mathrm{CE}\left(1-{\mathrm{e}}^{-\frac{-2\mathrm{t}}{\mathrm{RC}}}\right)$

Seven capacitors, a switch S and a source of e.m.f. are connected as shown in the figure. Initially, S is open and all capacitors are uncharged. After S is closed and steady state is attained, the potential difference in volt across the plates of the capacitor A is 

1. 12   
2. 15   
3. 17   
4. 19
 

A charge +q is fixed at each of the points x = x₀, x = 3x₀, x = 5x₀ ….. $\infty$ on the x-axis and a charge –q is fixed at each of the points x = 2x₀, x = 4x₀, x = 6x₀ …… $\infty$. Here, x₀ is a positive constant. Take the electric potential at a point due to charge Q at a distance r from it to be Q/4${\mathrm{\pi \epsilon }}_0$r. Then the potential at the origin due to the above system of charges is
1. zero
2. $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0{\mathrm{x}}_0\ln 2}$
3. $\infty$
4.  $\frac{\mathrm{qln}\left(2\right)}{4{\mathrm{\pi \epsilon }}_0{\mathrm{x}}_0}$

The equivalent capacitance of the network (with all capacitors having the same capacitance C) is  

1. $\infty$
2. zero
3. $\mathrm{C}\left(\frac{\sqrt{3}-1}{2}\right)$
4. $\mathrm{C}\left(\frac{\sqrt{3}+1}{2}\right)$

A part of the circuit is shown in the figure. All the capacitors have capacitance of 2mF. Then 

1. charge on capacitor C₁ is zero.                   
2. charge on capacitor C₂ is zero.                  
3. charge on capacitor C₃ is non-zero.
4. charge on capacitors cannot be determined.

Consider two concentric metal spheres. The outer sphere is given a charge Q> 0, then     

1. the inner sphere will be polarized due to field of the charge Q.
2. the electrons will flow from inner sphere to the earth if S is shorted.       
3. the shorting of S will produce a charge of –Qb/a on the inner sphere      
4. none of the above

In the circuit shown, the capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ have capacitance C each. The switch S is closed at time t = 0. Taking ${\mathrm{Q}}_0=\mathrm{CE}$ and $\mathrm{\tau }=\mathrm{RC}$ the charge on ${\mathrm{C}}_2$ after time t will be

1. ${\mathrm{Q}}_0\left(1-{\mathrm{e}}^{-\mathrm{t}/2\mathrm{\tau }}\right)$
2. ${\mathrm{Q}}_0\left(1-{\mathrm{e}}^{-\mathrm{t}/\mathrm{\tau }}\right)$
3. $\frac{{\mathrm{Q}}_0}{2}\left(1-{\mathrm{e}}^{-\mathrm{t}/2\mathrm{\tau }}\right)$
4. ${\mathrm{Q}}_0\left(1-{\mathrm{e}}^{-2\mathrm{t}/\mathrm{\tau }}\right)$

Two thin wire rings each having a radius R are placed at a distance d apart with their axis coinciding. The charges on the two rings are +Q and –Q. The potential difference between the centres of the two rings is 
1. zero
2. $\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+d^2}}\right]$
3. $\frac{\mathrm{QR}}{4{\mathrm{\pi \epsilon }}_0{\mathrm{d}}^2}$
4. $\frac{\mathrm{Q}}{2{\mathrm{\pi \epsilon }}_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+d^2}}\right]$

A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by $∆$T, the initial potential difference V across the capacitance 
1. $\sqrt{\frac{2\mathrm{mC}∆\mathrm{T}}{\mathrm{s}}}$
2. $\frac{\mathrm{mC}∆\mathrm{T}}{\mathrm{s}}$
3. $\frac{\mathrm{ms}∆\mathrm{T}}{C}$
4. $\sqrt{\frac{2\mathrm{ms}∆\mathrm{T}}{C}}$