Electrostatics

Ten charges are placed on the circumference
of a circle of radius R with constant angular
separation between successive charges.
Alternate charges 1, 3, 5, 7, 9 have charge (+q)
each, while 2, 4, 6, 8, 10 have charge (–q) each.
The potentia...

A two point charges 4q and -q are fixed
on the x-axis at x = \(- {d \over 2}\)
and x = \({d \over 2}\)
respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of t...

Two charged thin infinite plane sheets of uniform surface charge density \({\sigma _ + }\) and \({\sigma _ - }\), where |\({\sigma _ + }\)| > |\({\sigma _ - }\)|, intersect at right angle. Which of the following best represents the
electri...

A particle of charge q and mass m is subjected to an electric field E = E0
(1 – \(a\)x2) in the x-direction,
where \(a\) and E0
are constants. Initially the particle was at rest at x = 0. Other than the initial
position the kinetic energy...

Two isolated conducting spheres S1 and S2 of
radius \({2 \over 3}R\) and \({1 \over 3}R\) have 12 \(\mu\)C and –3 \(\mu\)C
charges, respectively, and are at a large
distance from each other. They are now
connected by a conducting wire. A ...

Concentric metallic hollow spheres of radii R and 4R hold charges Q1
and Q2
respectively. Given that
surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

A charged particle (mass m and charge q)
moves along X-axis with velocity V0. When it
passes through the origin it enters a region
having uniform electric field
\(\overrightarrow E = - E\widehat j\) which
extends upto x = d. Equation of ...

A small point mass carrying some positive
charge on it, is released from the edge of a
table. There is a uniform electric field in this
region in the horizontal direction. Which of the
following options then correctly describe the
trajector...

A charge Q is distributed over two concentric
conducting thin spherical shells radii r and
R (R > r). If the surface charge densities on the
two shells are equal, the electric potential at
the common centre is :

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :

Two point charges q1\(\left( {\sqrt {10} \mu C} \right)\) and q2(\(-\) 25 \(\mu\)C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take $${1 \over {4\pi { \in _0...

Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},\) where A and a are constants. If Q is the total charge of this charge distribution, the radi...

A system of three charges are placed as shown
in the figure :

If D >> d, the potential energy of the system is
best given by :

Four point charges –q, +q, +q and –q are placed
on y-axis at y = –2d, y = –d, y = +d and
y = +2d, respectively. The magnitude of the
electric field E at a point on the x-axis at
x = D, with D >> d, will behave as :-

The bob of a simple pendulum has mass 2g and
a charge of 5.0 μC. It is at rest in a uniform
horizontal electric field of intensity 2000 V/m.
At equilibrium, the angle that the pendulum
makes with the vertical is : (take g = 10 m/s2)

A solid conducting sphere, having a charge Q,
is surrounded by an uncharged 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 t...

The electric field in a region is given by
\(\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge\)
, where E is in NC–1 and x is in
metres. The values of constants are
A = 20 SI unit and B = 10 SI unit. If the potent...

A positive point charge is released from rest at
a distance r0 from a positive line charge with
uniform density. The speed (v) of the point
charge, as a function of instantaneous distance
r from line charge, is proportional to :-

There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(...

Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

A point dipole \(\overrightarrow p = - {p_0}\widehat x\)
is kept at the origin. The potential and electric field due to this dipole on the
y-axis at a distance d are, respectively: (Take V= 0 at infinity)

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge
Q. At its centre is a dipole \(\overrightarrow P\)
as shown. In this case :

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by \(\rho\)(r) = kr, where
r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite
points, at equa...

Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :

The given graph shows variation (with distance r form centre) of :

An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?

Two electric dipoles, A, B with respective dipole moments \({\overrightarrow d _A} = - 4qai\) and \({\overrightarrow d _B} = - 2qai\) are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both ...

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r ...

Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experience...

Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -

A uniformly charged ring of radius 3a and total
charge q is placed in xy-plane centred at origin.
A point charge q is moving towards the ring
along the z-axis and has speed u at z = 4a. The
minimum value of u such that it crosses the
origin...

In free space, a particle A of charge 1\(\mu\)C is held fixed at a point P. Another particle B of the same charge and
mass 4\(\mu\)g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P
is...

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touh...

A charge \(Q\) is placed at a distance \(a/2\) above the center of the square surface of edge a as shown in the figure. The electric flux through the square surface is

A body of mass \(M\) and charge \(q\) is connected to spring of spring constant \(k.\) It is oscillating along \(x\)-direction about its equilibrium position, taken to be at \(x=0,\) with an amplitude \(A\). An electric field \(E\) is appl...

A solid ball of radius R has a charge density \(\rho\)
given by \(\rho\) = \(\rho\)o (1 \(-\) \({\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}\)) for 0 \(\le\) r \(\le\) R. The ele...

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge
densities \(+ \sigma\), \(- \sigma\) and \(+ \sigma\) respectively. The potential of shell B is :

Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surfaces be \({\Phi _1},\) \({\Phi _2},\) \({\Phi _3}\) and \({\Phi _4}\). Then :

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P,\) in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere wh...

An electric dipole has a fixed dipole moment \(\overrightarrow p\), which makes angle \(\theta\) with respect to x-axis. When
subjected to an electric field \(\mathop {{E_1}}\limits^ \to = E\widehat i\) , it experiences a torque $$\over...

The potential (in volts) of a charge distribution is given by.
V(z) = 30 \(-\) 5x2 for \(\left| z \right|\) \(\le\) 1 m.
V(z) = 35 \(-\) 10 \(\left| z \right|\) for \(\left| z \right|\) \(\ge\)1 m.
V(z) does not depend on x and y. If t...

Within a spherical charge distribution of charge density \(\rho\)(r), N equipotential surfaces of potential V0, V0 + \(\Delta\)V, V0 + 2\(\Delta\)V, .......... V0 + N\(\Delta\)V (\(\Delta\) V > 0), are drawn and have increasing radii r...

The region between two concentric spheres of radii \('a'\) and \('b',\) respectively (see figure), have volume charge density \(\rho = {A \over r},\) where \(A\) is a constant and \(r\) is the distance from the center. A such that the elec...

A uniformly charged solid sphere of radius \(R\) has potential \({V_0}\) (measured with respect to \(\infty\)) on its surface. For this sphere the equipotential surfaces with potentials $${{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}}...

A long cylindrical shell carries positives surfaces change \(\sigma\) in the upper half and negative surface charge - \(\sigma\) in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures ar...

Assume that an electric field \(\overrightarrow E = 30{x^2}\widehat i\) exists in space. Then the potential difference \({V_A} - {V_O},\) where \({V_O}\) is the potential at the origin and \({V_A}\) the potential at \(x=2\) \(m\) is :

Two charges, each equals to \(q,\) are kept at \(x=-a\) and \(x=a\) on the \(x\)-axis. A particle of mass \(m\) and charge \({q_0} = {q \over 2}\) is placed at the origin. If charge \({q_0}\) is given a small displacement $$\left( {y < < ...

A charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

This question has statement- \(1\) and statement- \(2.\) Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius \(R\) has a uniformly positive charge densit...