Electrostatics

Two uniformly charged spherical conductors \(A\) and \(B\) of radii \(5 \mathrm{~mm}\) and \(10 \mathrm{~mm}\) are separated by a distance of \(2 \mathrm{~cm}\). If the spheres are connected by a conducting wire, then in equilibrium conditi...

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields E1 and E2 at...

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.

The volume charge density of a sphere of radius \(6 \mathrm{~m}\) is \(2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}\). The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$\times 10^{10}...

A vertical electric field of magnitude 4.9 \(\times\) 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :
(Given : g = 9.8 m/s2)

A long cylindrical volume contains a uniformly distributed charge of density \(\rho\). The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

Two identical charged particles each having a mass 10 g and charge 2.0 \(\times\) 10\(-\)7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction bet...

Two particles A and B having charges 20\(\mu\)C and \(-\)5\(\mu\)C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Choose the incorrect statement :(1) The electric lines of force entering into a Gaussian surface provide negative flux.(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.(3) In a uniform elec...

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '\(\theta\)' with the vertical?

What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?

A uniformly charged disc of radius R having surface charge density \(\sigma\) is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-

Figure shows a rod AB, which is bent in a 120\(^\circ\) circular arc of radius R. A charge (\(-\)Q) is uniformly distributed over rod AB. What is the electric field \(\overrightarrow E\) at the centre of curvature O ?

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = \({{\sqrt 3 } \over 2}L\).

An inclined plane making an angle of 30\(^\circ\) with the horizontal is placed in a uniform horizontal electric field \(200{N \over C}\) as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a he...

Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.Statement II : ...

27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is __________ times that of a smaller drop.

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field \(\overrightarrow E\) as a function of...

The two thin coaxial rings, each of radius 'a' and having charges +Q and \(-\)Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through dista...

Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle ...

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

The electric field in a region is given by \(\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}\). The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (par...

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is \({a \over {21}} \times {10^{ - 8}}\)C. The va...

Two identical conducting spheres with negligible volume have 2.1 nC and \(-\)0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ______...

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field \(\overrightarrow E\) through the shaded area is :

A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is \(-\)Q. The electric field at the centre of cube is :

A point charge of +12\(\mu\)C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ \(\times\) 103 Nm2/C.

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion...

The total charge enclosed in an incremental volume of 2 \(\times\) 10\(-\)9 m3 located at the origin is ___________ nC, if electric flux density of its field is found asD = e\(-\)x sin y \(\widehat i\) \(-\) e\(-\)x cos y \(\widehat j\) + 2...

An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 \(\times\) 10\(-\)6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from t...

A certain charge Q is divided into two parts q and (Q \(-\) q). How should the charges Q and q be divided so that q and (Q \(-\) q) placed at a certain distance apart experience maximum electrostatic repulsion?

A body having specific charge 8 \(\mu\)C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally tow...

A cube is placed inside an electric field, \(\overrightarrow E = 150{y^2}\widehat j\). The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

An oil drop of radius 2 mm with a density 3g cm\(-\)3 is held stationary under a constant electric field 3.55 \(\times\) 105 V m\(-\)1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will poss...

An infinite number of point charges, each carrying 1 \(\mu\)C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............The total force on a 1C point charge, placed at the origin, is x \(\times\) 103 N.The value of x, to ...

The electric field in a region is given by \(\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j\) with \({E_0} = 4.0 \times {10^3}{N \over C}\). The flux of this field through a rectangular surface area 0.4 m2 para...

Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.

Consider a sphere of radius R which carries a
uniform charge density \(\rho\). If a sphere of radius \({{R \over 2}}\) is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {...

An electric dipole of moment
\(\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}}\) C.m is at the origin
(0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \wideha...

An electric field \(\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j\) N/C
passes through the box shown in figure. The
flux of the electric field through surfaces ABCD
and BCGF are marked as \({\phi _I}\) and $${\phi...

In finding the electric field using Gauss Law
the formula \(\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}\) is applicable. In the
formula \({{\varepsilon _0}}\) is permittivity of free space, A...

Three charged particle A, B and C with charges
–4q, 2q and –2q are present on the
circumference of a circle of radius d. the charged
particles A, C and centre O of the circle formed
an equilateral triangle as shown in figure. Electric
field...

Consider two charged metallic spheres S1 and
S2 of radii R1 and R2, respectively. The electric
fields E1 (on S1) and E2 (on S2) on their surfaces
are such that E1/E2 = R1/R2. Then the ratio
V1 (on S1) / V2 (on S2) of the electrostatic
poten...

A particle of mass m and charge q is released
from rest in a uniform electric field. If there is
no other force on the particle, the dependence
of its speed v on the distance x travelled by it
is correctly given by (graphs are schematic and...

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the region shown between them is given by :

Charges Q1
and Q2
are at points A and B of a right angle triangle OAB (see figure). The resultant
electric field at point O is perpendicular to the hypotenuse, then \({{{Q_1}} \over {{Q_2}}}\)
is proportional to :

Two identical electric point dipoles have dipole moments \({\overrightarrow p _1} = p\widehat i\) and \({\overrightarrow p _2} = - p\widehat i\) and are held on the x
axis at distance '\(a\)' from each other. When released, they move along...

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying
charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is
placed at distance r from the centre...

A solid sphere of radius R carries a charge
Q + q distributed uniformly over its volume. A
very small point like piece of it of mass m gets
detached from the bottom of the sphere and
falls down vertically under gravity. This piece
carries c...