The potential gradient is a:

The electric potential V at a point P(x, y, z) in space is given by $\mathrm{V}=4{\mathrm{x}}^2$ volt. The electric field at a point (1m, 0, 2m) in V/m is:

Determine the electric field strength vector if the potential of this field depends on x, y coordinates as V=10axy.

If on the x-axis, the electric potential decreases uniformly from 60 V to 20 V between x=-2 m to x=+2 m, then the magnitude of electric field at the origin:

An infinite conducting sheet has a surface charge density $\mathrm{\sigma }$. The distance between the two equipotential surface is r. The potential difference between these two surfaces is:

If an $\mathrm{\alpha }$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt, then the ratio of their kinetic energies will be:

Three charges -q, Q and -q are placed respectively at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q?

A particle A has charge +q and another particle B has charge +4q with each of them having the same mass m. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds $\frac{{\mathrm{v}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{B}}}$ will become:

If 50 joule of work must be done to move an electric charge of 2 C from a point where the potential is -10 volt to another point where the potential is V volt, then the value of V is:

A proton has a mass $1.67\times {10}^{-27}$ kg and a charge $+1.6\times {10}^{-19}$ C. If the proton is accelerated through a potential difference of 1 million volts, then the kinetic energy is:

Two electrons are moving towards each other, each with a velocity of ${10}^6$ m/s. What will be the closest distance of approach between them?

1000 small water drops, each of capacitance C, join together to form one large spherical drop. The capacitance of the bigger sphere is:

Two similar conducting balls having charges +q and -q are placed at a separation d from each other in the air. The radius of each ball is r and the separation between their centres is d(d>>r). Calculate the capacitance of the two-ball system.

Two parallel plate capacitors have their plate areas 100 cm² and 500 cm² respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is 0.5 mm, then the distance between the plates of the second capacitor is:

A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacitor carrying charge q. The induced charge q' on the surface of the slab is given by:

The following arrangement consists of five identical metal plates parallel to each other. The area of such plate is A and separation between the successive plates is d. The capacitance between P and Q is:

The charge on the 6 $\mathrm{\mu F}$ capacitors in the circuit shown is:

In a region of constant potential:
a. the electric field is uniform
b. the electric field is zero
c. there can be no charge inside the region
d. the electric field shall necessarily change if a charge is placed outside the region

In the circuit shown below ${\mathrm{C}}_1=10\mathrm{\mu F}, {\mathrm{C}}_2={\mathrm{C}}_3=20\mathrm{\mu F}$ and ${\mathrm{C}}_4=40\mathrm{\mu F}$. If the charge on C₁ is $20\mathrm{\mu C}$ then potential difference between X and Y is 

A capacitor with plate separation d is charged to V volts. The battery is disconnected and a dielectric slab of thickness $\frac{\mathrm{d}}{2}$ and dielectric constant '2' is inserted between the plates. The potential difference across its terminals becomes:

An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air-cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V'. The dielectric constant K is:

A battery does 200 J of work in charging a capacitor. The energy stored in the capacitor is:

Two identical capacitors are connected in parallel across a potential difference V. After they are fully charged, the positive plate of the first capacitor is connected to the negative plate of the second and the negative plate of the first is connected to the positive plate of the other. The loss of energy will be:

Figure shows equipotential surfaces for a two charges system. At which of the labeled points will an electron have the highest potential energy?

A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q₁ is placed outside it as shown in the figure. All the three charges are positive. The force on the central charge due to the shell is:

In a certain region of space, the electric field is zero. From this we can conclude that the electric potential in this region is:

An uncharged aluminium block has a cavity within it. The block is placed in a region permeated by a uniform electric field which is directed upwards. Which of the following is a correct statement describing conditions in the interior of the block's cavity?

A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is U. Now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. The work performed against the forces of the electric field in pulling out the insulator is 4U. Then dielectric constant of the insulator is:

An insulator plate is passed between the plates of a capacitor. Then current(outside the capacitor):

For a uniform spherical positive distribution of charge over volume of radius R, the potential will be maximum: