Marks 1
As shown in the figure below, to concentric conducting spherical shells, centred at r = 0 and having radii r = c and r = d are maintained at potential...
A positive charge of 1 nC 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...
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 b...
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 ...
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) ...
Consider a function $$\overrightarrow f=\frac1{r^2}\widehat r$$ where r is the distance from the origin and $$\widehat r$$ is the unit
vector in the r...
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 ...
A parallel plate capacitor consisting two dielectric materials is shown in the figure. The
middle dielectric slab is place symmetrically with respect ...
Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is
Divergence of the vector field
$$$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;...
A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$mm$$ space between the plates i...
Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that
In a uniform electric field, field lines and equipotentials
If v, w, q stand for voltage, energy and charge, then v can be expressed
In electrostatic field $$\nabla\times\overrightarrow E\equiv0$$
Which of the following equations represents the Gauss's law in a homogeneous isotropic medium?
An electrostatic potential is given by $$\phi=2x\sqrt y$$ volt in the rectangular co-ordinate system. The magnitude of the electric field at x = 1 m,y...
Marks 2
The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab
whose thickness is half the distance between the plates, is...
A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm(a << R), is at a potential of 1
V with respect to a reference point at infinity....
Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the
zero equipotential curve in the x-y plane is
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +𝑄 is placed at a distance of ...
A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 ...
A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system.
A charge of $$+32{\mathrm{πε}}_0\sqrt2$$ columbs is pla...
A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is
subjected to a uniform electric field of $$E=6{\widehat a}_x+8{\wideha...
A capacitor is made with a polymeric dielectric having an $$\varepsilon_0$$ of 2.26 and a
dielectric breakdown strength of 50 kV/cm. The permittivity ...
$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line ...
A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled...
Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( { - 1, - 1,0} \right)$$ respe...
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 ...
A parallel plate capacitor has an electrode area of $$100$$ $$m{m^2}$$, with a spacing of $$0.1$$ $$mm$$ between the electrodes. The dielectric betwee...
A point charge of $$+1$$ $$nC$$ is placed in a space with a permittivity of $$8.85 \times {10^{ - 12}}\,F/m$$ as shown in Fig. The potential differenc...
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($${t_1}$$ and $${t_2}$$) as shown in F...
The electric field $$\overrightarrow E $$ (in volts/metre) at the point $$(1, 1, 0)$$ due to a point charge of $$+1$$ $$\mu C$$ located at $$\left( {...
Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts ...
The capacitance of an isolated sphere of radius 10 cm in air is equal to _____ pF.
The capacitance of the arrangement shown in Fig. is ................... $$pF$$
...
Marks 5
Show via the construction of a suitable Gaussian surface, that the capacitance of a spherical capacitor consisting of two concentric shells of radii ...
A charge $$+Q$$ is uniformly distributed throughout the volume of a dielectric sphere of radius $$R$$ and dielectric constant $$'{\varepsilon _R}'.$$ ...
An infinite number of charges, each equal to $$'q'$$ are placed along the $$x=1,x=2, x=4, x=8, x=16$$ and so on, Find the potential and electric field...
Determine the electric field intensity at the point $$P$$ for the arrangement shown in Fig.
...