Five identical plates each of area A are joined as shown in the figure. The distance between the plates is d. The plates are connected to a potential difference of \[V\ volts\]. The charge on plates 1 and 4 will be [IIT 1984]

\[\frac{-{{\varepsilon }_{0}}AV}{d}.\frac{-2{{\varepsilon }_{0}}AV}{d}\]

\[\frac{{{\varepsilon }_{0}}AV}{d}.\frac{2{{\varepsilon }_{0}}AV}{d}\]

\[\frac{-{{\varepsilon }_{0}}AV}{d}.\frac{-2{{\varepsilon }_{0}}AV}{d}\]

A solid metallic sphere has a charge \[+\,3Q\]. Concentric with this sphere is a conducting spherical shell having charge \[-Q\]. The radius of the sphere is \[a\] and that of the spherical shell is \[b(b>a)\]. What is the electric field at a distance \[R(a

\[\frac{4Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

\[\frac{Q}{2\pi {{\varepsilon }_{0}}R}\]

\[\frac{3Q}{2\pi {{\varepsilon }_{0}}R}\]

\[\frac{4Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of ?3Q, the new potential difference between the same two surfaces is [IIT 1989]

Is zero along all the paths \[AB,\ AC,\ AD\] and \[AE\]

Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when [MP PET 2002]

Net induced charge on the sphere is zero

Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible [AMU 2001]

\[|{{\overrightarrow{E}}_{1}}|\,=\,|{{\overrightarrow{E}}_{2}}|,\ {{V}_{1}}={{V}_{2}}\]

\[{{\overrightarrow{E}}_{1}}\ne {{\overrightarrow{E}}_{2}},\ {{V}_{1}}\ne {{V}_{2}}\]

\[|{{\overrightarrow{E}}_{1}}|\,=\,|{{\overrightarrow{E}}_{2}}|,\ {{V}_{1}}\ne {{V}_{2}}\]

A non-conducting solid sphere of radius \[R\] is uniformly charged. The magnitude of the electric field due to the sphere at a distance \[r\] from its centre [IIT-JEE 1998; DPMT 2000]

Increases as \[r\] increases for \[r

Decreases as \[r\] increases for \[0

Two point charges \[\text{3}\times \text{1}{{0}^{\text{6}}}C\]and \[\text{8}\times \text{1}{{0}^{\text{6}}}C\] repel each other by a force of \[\text{6}\times \text{1}{{0}^{\text{3}}}N\]. If each of them is given an additional charge \[\text{ 6}\times \text{1}{{0}^{\text{6}}}C\], the force between them will be [DPMT 2003]

\[2.4\times \text{1}{{0}^{3}}N\] (attractive)

\[2.4\times \text{1}{{0}^{9}}N\] (attractive)

\[\text{1}.\text{5}\times \text{1}{{0}^{\text{3}}}N\] (attractive)

A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself [MP PMT 1991]

Such that the total heat loss is minimized

Uniformly on the surface of the object

\[13.5\times {{10}^{6}}\] N/C directed towards \[+5\mu C\]

Such that the total heat loss is minimized

A parallel plate condenser with oil between the plates (dielectric constant of oil \[K=2\]) has a capacitance\[C\]. If the oil is removed, then capacitance of the capacitor becomes [CBSE PMT 1999; MH CET 2000]

\[E\propto \frac{1}{{{r}^{2}}}\]

The plates of a parallel plate capacitor of capacity \[50\mu C\] are charged to a potential of \[100\ volts\] and then separated from each other so that the distance between them is doubled. How much is the energy spent in doing so [MP PET 1997; JIPMER 2000]

\[\frac{P}{4\pi {{\varepsilon }_{0}}{{r}^{3}}}\]

The energy stored in a condenser of capacity \[C\] which has been raised to a potential \[V\]is given by [MP PMT 1993; CPMT 1974; DCE 2002; RPET 2003]

\[7.68\times {{10}^{-29}}\ coulomb\times m\]

In a spherical condenser radius of the outer sphere is \[R\]. The different in the radii of outer and inner sphere in\[x\]. Its capacity is proportional to

\[\frac{q\sqrt{2}({{Q}_{1}}+{{Q}_{2}})}{4\pi {{\varepsilon }_{0}}R}\]

The electric field between the two spheres of a charged spherical condenser [MP PMT 1994]

Decreases with distance from the centre

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then [IIT 1987; MP PET 1992; Manipal MEE 1995; MP PMT 1996]

The charge on the capacitor increases

The voltage across the plates decreases

\[\frac{2{{\varepsilon }_{0}}A}{3d}\]

The electrostatic energy stored in the capacitor increases

As shown in the figure, a very thin sheet of aluminium is placed in between the plates of the condenser. Then the capacity [AIEEE 2003]

\[\,\frac{{{\varepsilon }_{0}}AV}{d}.\frac{-2{{\varepsilon }_{0}}AV}{d}\]

Force of attraction between the plates of a parallel plate capacitor is [AFMC 1998]

\[\frac{{{q}^{2}}}{{{\varepsilon }_{0}}AK}\]

\[\frac{{{q}^{2}}}{2{{\varepsilon }_{0}}AK}\]

\[\frac{{{q}^{2}}}{{{\varepsilon }_{0}}AK}\]

\[\frac{{{q}^{2}}}{2{{\varepsilon }_{0}}{{A}^{2}}K}\]

The capacity of a condenser is \[4\times {{10}^{-6}}\] farad and its potential is\[100\,\,volts\]. The energy released on discharging it fully will be [AFMC 1988; AIIMS 1980, 84]

\[\frac{3Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

Between the plates of a parallel plate condenser, a plate of thickness \[{{t}_{1}}\]and dielectric constant \[{{k}_{1}}\] is placed. In the rest of the space, there is another plate of thickness \[{{t}_{2}}\] and dielectric constant \[{{k}_{2}}\]. The potential difference across the condenser will be [MP PET 1993]

\[\frac{{{\varepsilon }_{0}}Q}{A}\left( \frac{{{t}_{1}}}{{{k}_{1}}}+\frac{{{t}_{2}}}{{{k}_{2}}} \right)\]

\[\frac{Q}{A{{\varepsilon }_{0}}}\left( \frac{{{t}_{1}}}{{{k}_{1}}}+\frac{{{t}_{2}}}{{{k}_{2}}} \right)\]

\[\frac{{{\varepsilon }_{0}}Q}{A}\left( \frac{{{t}_{1}}}{{{k}_{1}}}+\frac{{{t}_{2}}}{{{k}_{2}}} \right)\]

\[\frac{{{\varepsilon }_{0}}Q}{A}({{k}_{1}}{{t}_{1}}+{{k}_{2}}{{t}_{2}})\]

The radius of two metallic spheres \[A\] and \[B\] are \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively \[({{r}_{1}}>{{r}_{2}})\]. They are connected by a thin wire and the system is given a certain charge. The charge will be greater

\[{{\overrightarrow{E}}_{1}}\ne {{\overrightarrow{E}}_{2}},\ {{V}_{1}}={{V}_{2}}\]

On the surface of the sphere \[B\]

On the surface of the sphere \[A\]

\[{{\overrightarrow{E}}_{1}}\ne {{\overrightarrow{E}}_{2}},\ {{V}_{1}}={{V}_{2}}\]

The unit of electric permittivity is [MP PET 2003]

Decreases as \[r\] increases for \[R

The capacitance of a spherical condenser is \[1\mu F\]. If the spacing between the two spheres is\[1\,mm\], then the radius of the outer sphere is [CPMT 1989]

\[\text{1}.\text{5}\times \text{1}{{0}^{\text{3}}}N\] (repulsive)

If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to [AIEEE 2002]

Such that the potential energy of the system is minimized

The mean electric energy density between the plates of a charged capacitor is (here \[q\]= charge on the capacitor and \[A\]= area of the capacitor plate) [MP PET 2002]

\[\frac{q}{2{{\varepsilon }_{0}}{{A}^{2}}}\]

\[\frac{{{q}^{2}}}{2{{\varepsilon }_{0}}{{A}^{2}}}\]

\[\frac{q}{2{{\varepsilon }_{0}}{{A}^{2}}}\]

Two insulated charged spheres of radii \[20\,cm\] and \[25\,cm\]respectively and having an equal charge \[Q\] are connected by a copper wire, then they are separated [NCERT 1971]

Charge on each of the sphere will be \[2Q\]

Both the spheres will have the same charge \[Q\]

Charge on the \[20\ cm\] sphere will be greater than that on the \[25\ cm\] sphere

Charge on each of the sphere will be \[2Q\]