Between the plates of a parallel plate capacitor a dielectric plate is introduced just to fill the space between the plates. The capacitor is charged and later disconnected from the battery. The dielectric plate is slowly drawn out of the capacitor parallel to the plates. The plot of the potential difference across the plates and the length of the dielectric plate drawn out is

Equipotential surfaces are shown in figure. Then the electric field strength will be

A condenser of 2μF capacitance is charged steadily from 0 to 5 Coulomb. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the condenser?

In an RC circuit while discharging, the graph of log i versus time is as shown by the dotted line in the diagram figure, where i is the current. When the value of the resistance is doubled, which of the solid curve best represents the variation of log i versus time ?

Figure shows a solid hemisphere with a charge of 5nC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15 cm. The electric potential at point P due to the hemisphere, is –

A point charge Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R. The potential of the sphere is (d > R) –

An electric field is given by ${\mathrm{E}}_{\mathrm{x}} = – 2{\mathrm{x}}^3 \mathrm{kN}/\mathrm{C}$. The potential of the point (1, –2), if potential of the point (2, 4) is taken as zero, is –

A conducting disc of radius R is rotating about its axis with an angular velocity $\mathrm{\omega }$. Then the potential difference between the centre of the disc and its edge is (no magnetic field is present)

A uniform electric field of 400 V/m exists in space as shown in graph. Two points A and B are also shown with their co-ordinates. The potential difference ${\mathrm{V}}_{\mathrm{B}} – {\mathrm{V}}_{\mathrm{A}}$ in volts, is – 

Figure shows three circular arcs, each of radius R and total charge as indicated. The net electric potential at the centre of curvature is –

A neutral conducting spherical shell is kept near a charge q as shown. The potential at point P due to the induced charges is –

Two concentric uniformly charged spheres of radius 10 cm and 20 cm. are arranged as shown in figure. Potential difference between the sphere is –

In a uniform field – 

Two metallic bodies separated by a distance of 20 cm, are given equal and opposite charges of the magnitude of 0.88$\mu$C. The component of the electric field along the line AB, between the plates, varies as, ${\mathrm{E}}_{\mathrm{x}}=(3{\mathrm{x}}^2 + 0.4) \mathrm{N}/\mathrm{C}$ where x (in meters) is the distance from one body towards the other body as shown.

Electrical potential ‘v’ in space as a function of coordinates is given by, $\mathrm{v}=\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{z}}$ . Then the electric field intensity at (1, 1, 1) is given by –

Two concentric, thin metallic spheres of radii ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ $\left({\mathrm{R}}_1 > {\mathrm{R}}_2\right)$ bear changes ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ respectively. Then the potential at distance r between ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ will be $\left(\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\right)$

The grid (each square of 1m × 1m), represents a region in space containing a uniform electric field.

If potentials at points O, A, B, C, D, E, F and G, H are respectively 0, –1, –2, 1, 2, 0, –1, 1 and 0 volts, find the electric field intensity –

Figure shows an electric line of force which curves along a circular arc.

The magnitude of electric field intensity is same at all points on this curve and is equal to E. If the potential at A is V, then the potential at B is –

A parallel plate capacitor with air between the plates is charged to a potential difference of 500V and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes 75V. The dielectric constant of plastic is –

The circuit was in the shown state for a long time. Now if the switch S is closed then the charge that flows through the switch S, will be –

A capacitor of $1 \mu \mathrm{F}$ withstands a maximum voltage of 6 kilovolts while another capacitor of $2 \mu \mathrm{F}$ withstands a maximum voltage of 4 kilovolts. If the two capacitors are connected in series, the system will withstand a maximum voltage of:

The potential at a certain point in an electric field is 200 V. The work done in carrying an electron upto that point will be.

Two charged conducting spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ are at the same potential. The ratio of their surface charge densities will be -

At the mid point of a line joining an electron and a proton, the values of E and V will be.

A charge of $10\mu \mathrm{C}$ is kept at the origin of $\mathrm{X}–\mathrm{Y}$ coordinate system. The potential difference in volts between two points (a, 0) and $\left(\mathrm{a}/\sqrt{2} , \mathrm{a}/\sqrt{2}\right)$ will be.

Find equivalent capacitance between $\mathrm{X}$ and $\mathrm{Y}$ if each capacitor is $4 \mathrm{\mu F}$.

Two point charge of $8 \mathrm{\mu C}$ and $12 \mathrm{\mu C}$ are kept in air at a distance of 10 cm from each other. The work required to change the distance between them to 6 cm will be.

Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes –

Maximum charge stored on a metal sphere of radius $15$ cm may be $7.5 \mu \mathrm{C}$. The potential energy of the sphere in this case is :

Four identical particles each of mass m and charge q are kept at the four corners of a square of length L. The final velocity of these particles after setting them free will be.