Electric potential and capacitance practice · Mixed difficulty

When a dielectric slab is introduced between the plates of a capacitor connected to a battery, then

The electric potential is $+100 \mathrm{~V}$ at a distance of $10 \mathrm{~cm}$ from a point charge $\text{q}.$ Then, $\text{q}$ is equal to

Two spheres of radii 12 cm and 16 cm have equal charge. The ratio of their energies is

Assertion (A) : A small electric dipole is moved translationally from higher potential to lower potential in uniform electric field. Work done by electric field is positive.

Reason (R) : When a positive charge is moved from higher potential to lower potential, work done by electric field is positive.

A sphere of radius 0.03 mis suspended within a hollow sphere of radius $0.05 \mathrm{~m}$. If the inner sphere is charged to a potential of 1500 volt and outer sphere is earthed, find the capacitance and the charge on the inner sphere.

An electric dipole consists of two opposite charges each 0.05$\mathrm{\mu C}$ separated by 30 mm. The dipole is placed in an uniform external electric field of ${10^6}\mathrm{N}{\mathrm{C}^{ - 1}}.$ The maximum torque exerted by the field on the dipole is

A $6\,\mu F$ capacitor is charged to 200 V. If its plates are joined through a resistance of $4\,K\Omega ,$ then heat produced in the resistance is

Taking the Earth to be a spherical conductor of diameter $12.8 \times 10^3 \mathrm{~ k m}.$ Its capacity will be

If a slab of insulating material $4 \times {10^{ - 3}}m$ thick is introduced between the plates of a parallel plate capacitor, the separation between plates has to be increased by $3.5 \times {10^{ - 3}}m$ to restore the capacity to original value. The dielectric constant of the material will be

Electric field is given by $E=\frac{100}{x^2}$ potential difference between $x=10$ and $x=20 \mathrm{~m}$.

When charge of magnitude $10 \mu \mathrm{C}$ is shifted from infinity to a point in an electric field, then it was found that work done by electrostatic forces is $-10 \mu \mathrm{J}$. If this charge is doubled and moved again from infinity to the same point without changing its velocity, then find out the work done by electric field and against this electric field.

The electric potential at the centre of a charged
conductor is

Electric potential at any point is $V = - 5x + 3y + \sqrt {15z} ,$ then the magnitude of the electric field is

A condenser has a capacity $2 \mu \mathrm{F}$ and is charged to a voltage of $50 \mathrm{~V}.$ The energy stored is

A metallic hollow sphere of radius $3 \mathrm{~cm}$ is charged so that potential at its surface is $5 \mathrm{~V}.$ The potential at the centre of sphere will be

A ring with uniform distribution of charge $q$ and radius $a$ is placed in $Y-Z$ plane with its centre at origin.

The separation between the plates of a charged parallel- plate capacitor is increased. The force between the plates

Capacitance of a parallel plate capacitor becomes $\frac{4}{3}$ times its original value, if a dielectric slab of thickness $t = \frac{d}{2}$ is inserted between the plates [$d$ is the separation between the plates]. The dielectric constant of the slab is

Two equal charges ‘q’ of opposite sign are separated by small distance ‘2a’. The electric intensity ‘E’ at a point on the perpendicular bisector of the line joining the two charges at a very distance ‘r’ from the line is

Assertion:- A parallel plate capacitor is connected across a battery through a key. A dielectric slab of dielectric constant $K$ is introduced between the plates. The energy which is stored becomes $K$ times.
Reason:- The potential difference between the plates remains constant or unchanged.

A parallel plate capacitor with plate area $A$ and distance of separation $d$ is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as
$\varepsilon \,(X) = {\varepsilon _0} + \,\,kx,$ for $\left( {0 < x \le \frac{d}{2}} \right)$
$\varepsilon \,(X)\,\, = \,\,{\varepsilon _0} + k\,(d - x)$ for $\left( {\frac{d}{2} \le x \le d} \right)$

A sample of $\mathrm{HCl}$ gas is placed in an electric field of $2.5 \times 10^4 \mathrm{~N} \mathrm{C}^{-1}$. The dipole moment of each $\mathrm{HCl}$ molecule is $3.4 \times 10^{-30} \mathrm{Cm}$. Find the maximum torque that can act on a molecule.

A point $A$ is at potential $+500 \mathrm{~Volt}$ and $B$ is a point of potential $-500 \mathrm{~Volt}.$ The work done by an external agent to take a unit positive charge from $A$ to $B$ is

You are given an arrangement of three point charges $q, 2 q$ and $x q$ separated by equal finite distances that electric potential energy of the system is zero. Then the value of $x$ is:

A uniform electric field of $100 \mathrm{~N} / \mathrm{C}$ exists in $\mathrm{XY}$ plane making an angle $60^{\circ}$ with $+\mathrm{x}$ direction. Consider points $A(1,2,3) \mathrm{m}$ and $B(3,2,1) \mathrm{m}$ then $\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}$ is:

The electric intensity due to a dipole of length 10 cm and having a charge of $500\,\,\mu C$ at a point on the axis at a distance 20 cm from one of the charges in air, is

Assertion:- Electric potential energy of any positive charge is always positive.
Reason:-Potential energy is a vector quantity.

Assertion: Electrings always move from a region of lower potential to a region of high potential.

Reason: Electrings carryy a negative charge.

Assertion:- The capacitance of a capacitor depends on the shape, size and geometrical placing of the conductors and the medium between them.
Reason:- When a charge $q$ passes through a battery of emf ${E}$ from the negative terminal to the positive terminal, an amount of work ${qE}$ is done by the battery.

A point charge is situated at an axial point of a small electric dipole at a large distance from it. The charge
experiences a force F. If the distance of the charge is doubled, the force acting on the charge will become