Which one of the following figures represents the radial electric field distribution  caused by a spherical cloud of electrons with a volume charge density,  for  (both  are positive and  is the radial distance) and  for  ?

Let  be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of , the divergence of the radial vector field  is independent of  ?

In the  coordinate system, three point-charges , and  are located in free space at , and , respectively. The value of  for the electric field to be zero at  is ________(rounded off to 1 decimal place).

Let . The value of , where V is the volume enclosed by the unit cube defined by 0 ≤ 𝑥 ≤ 1, 0 ≤ 𝑦 ≤ 1, and 0 ≤ 𝑧 ≤ 1, is

As shown in the figure below, two concentric conducting spherical shells, centered at r = 0 and having radii r = c and r= d are maintained at potentials such that the potential V(r) at r = c is  and V(r) at r = d is . Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

A  point charge is held at the origin of a cartesian coordinate system. If a second point charge of  is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is _______ mJ. (Round off to 2 decimal places).

Take  in SI units. All coordinates are in meters.        

Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field  in the gap to the original electric field  is __.

The vector function expressed by

represents a conservative field, where , ,  are unit vector along x, y and z directions, respectively. The values of constants , ,  are given by:

The static electric field inside a dielectric medium with relative permittivity, , expressed in cylindrical coordinate system is given by the following expression

where , ,  are unit vectors along r,  and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, , in SI units is given by:

Let ,  and  be unit vectors along r,  and z directions, respectively in the cylindrical coordinate system. For the electric flux density given by  , the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

A co-axial cylindrical capacitor shown in figure (i) has dielectric with relative permittivity. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity, as shown in Figure (ii), the capacitance is doubled. The value of  is ___

A positive charge of 1nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take . The Z component of the E field at (0, 0, 0.1) is closest to

The capacitance of an air-filled parallel-plate capacitor is 60pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _______ (up to 2 decimal places).        

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t = 0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?

The figures show diagrammatic representations of vector fields  . Respectively. Which one of the following choices is true?        

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed

A thin soap bubble of radius R = 1 cm, and thickness a = 3.3  ), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r . The volume of the soap in the thin bubble is  and that of the drop is . The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is ___________. (Give the answer up to two decimal places.)

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by , where f is a continuous function of r and z. Let  be the resulting electric field. Then the magnitude of

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

A parallel plate capacitor filled with two dielectric is shown in the figure below, If the electric field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is

Two electrodes, whose cross-sectional view is shown in figure below, are at the same potential. The maximum electric field will be at the point

A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strength of air and glass are 30kV/cm and 300kV/cm, respectively. The maximum voltage (in kilovolts) which can be applied across the capacitor without any breakdown is _____________.

Match the following:

Two semi – infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y < 0) and region 2(y > 0) are 2 and 5, respectively. Region 1 has uniform electric field  where and  are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is, where K is given by

is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity, the expression for the modified capacitance is

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is placed symmetrical with respect to the plates.

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio  is

A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R (> r) is

A perfectly conducting metal plate is placed in x-y plane in a right-handed coordinate system. A charge of  coulombs is placed at coordinate (0,  0, 2).  is the permittivity of free space. Assume   to be unit vectors along x, y and z axes, respectively. At the coordinate, the electric field vector  (Newtons/Columbs) will be

Three capacitors , , and , whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in volts that can be applied across the combination and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively         

A dielectric slab with 500mm × 500mm cross –section is 0.4m long. The slab is subjected to a uniform electric field of. is equal to 2. The value of constant  is . The energy stored n the dielectric in joules is

The direction of vector A is radially outward from the oigin, with  where  and k is a constant. The value of n for which  is

In the following figure,  and  are ideal capacitors.  has been charged to 12V before the ideal switch S is closed at t = 0. The current i(t) for all t is

A capacitor is made with a polymeric dielectric having an of 2.26 and a dielectric breakdown strength of 50kV/cm. The permittivity of free space is 8.85pF/m. If the rectangular plates of the capacitor have a width of 20cm and a length of 40cm, then the maximum electric charge in the capacitor is

A capacitor consists of two metal plates each  and spaced 6 mm apart. The space between the metal plates is filled with a glass plate of 4 mm thickness and a layer of paper of 2 mm thickness. The relative permittivity of the glass and paper are 8 and 2 respectively. Neglecting the fringing effect, the capacitance will be

(Given that )

Two point charges  and  are placed at coordinates (1, 1, 0) and (−1, −1, 0) respectively.  The total electric flux passing through a plane z = 20 will be

A solid sphere made of insulating material has a radius R and has a total charge Q distributed uniformly in its volume. What is the magnitude of the electric field intensity, E, at a distance r (0<r<R) inside the sphere?

An inductor designed with 400 turns coil wound on an iron core of  cross sectional area and with a cut of an air gap length of 1mm. The coil is connected to a 230 V, 50 Hz AC supply.  Neglect coil resistance, core loss, iron reluctance and leakage inductance

The current in the inductor is

An inductor designed with 400 turns coil wound on an iron core of  cross sectional area and with a cut of an air gap length of 1mm. The coil is connected to a 230 V, 50 Hz AC supply.  Neglect coil resistance, core loss, iron reluctance and leakage inductance

The average force on the core to reduce the air gap will be

If  is the electric field intensity,  is equal to

A parallel plate capacitor is shown in figure. It is made of two square metal plates of 400 mm side. The 14 mm space between the plates is filled with two layers of dielectrics of , 6 mm thick and , 8 mm thick.  Neglecting fringing of fields at the edges the capacitance is

A point charge of +1nC is placed in a space with a permittivity of  as shown in Figure. The potential difference  between two points P and Q at distances of 40 mm and 20 mm respectively from the point charge is

A parallel plate capacitor has an electrode area of , with a spacing of 0.1 mm between the electrodes. The dielectric between the plates is air with a permittivity of . The charge on the capacitor is 100 V. The stored energy in the capacitor is

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ( and ) as shown in Figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is

Given a vector field, the divergence theorem states that

The electric field  (in volts/metre) at the point (1, 1, 0) due to a point charge of +1µC located at (−1, 1, 1) (coordinates in metres) is  

Given the potential function in free space to be  volts, the magnitude (in volts/metre) and the direction of the electric field at a point (1, -1, 1), where the dimensions are in metres, are

When the plate area of a parallel plate capacitor is increased by keeping the capacitor voltage constant, the force between the plates         

A charge +Q uniformly distributed throughout the volume of a dielectric sphere of radius R and dielectric constant based on Gauss law, determine the expressions for the electric field E as a function of distance r from the centre of the sphere, within the ranges 0<r<R and . Indicate expression(s) for the critical point(s) on the sketch.

An infinite number of charges, each equal to ‘q’ are placed along the x=1, x=2 , x=4, x=8 , x=16 and so on. Find the potential and electron field at point x=0, due to these systems of charges.

In a uniform electric field, field lines and equipotentials

The capacitance of the arrangement shown in figure is ________ pF

The capacitance of an isolated sphere of radius 10cm in air is equal to ________ pF

Determine the electric field intensity at the point p for the arrangement shown in figure above

Insider a hollow conducting sphere

If v, w, q stand for voltage, energy and charge, then v can be expressed as

A spherical conductor of radius ‘a’ with charge ‘q’ is placed concentrically inside an uncharged and unearthed spherical conducting shell of inner and outer radii  respectively. Taking potential to be zero at infinity, the potential at any point P within the shell  will be:        

When a charge is given to a conductor

In an electrostatic field . ( True=1, False=0)

A hollow conductor is at a potential V. The potential at any point inside the hollow is V.  ( True=1, False=0)

Which of the following equations represents the Gauss’ law in a homogeneous isotropic medium?

An electrostatic potential is given by  volts in the rectangular co-ordinate system. The magnitude of the electric field at ,  is _____________ V/m