Electrostatic Potential and Capacitance

The potential energy of a system of two identical charges $q$ separated by distance $r$ is $U$. If the distance between them is increased to $2r$, the new potential energy is:

Two conducting spheres of different radii $R_1$ and $R_2$ ($R_1 > R_2$) are given the same amount of charge $Q$. Which sphere will have a higher electric potential at its surface?

In the diagram provided, point P lies on the perpendicular bisector (equatorial line) of an electric dipole consisting of charges $-q$ and $+q$. What is the electric potential at point P?

If a positive charge moves in the direction of the electric field lines, its electrostatic potential energy:

An electric dipole of moment $p$ is placed in a uniform electric field $E$. The maximum potential energy of the dipole is:

The potential gradient $dV/dx$ represents:

The potential energy of a system of three charges $q, q, -q$ placed at the corners of an equilateral triangle of side $a$ is:

Two charges $q$ and $-q$ are placed at $(d, 0)$ and $(-d, 0)$. The equation of the equipotential surface with $V = 0$ is:

The work done in blowing a soap bubble of radius $R$ and surface tension $T$ to a potential $V$ (assuming charge resides on the surface) is:

Twelve charges, each $q$, are placed at the corners of a regular 12-sided polygon. If one charge is removed, the change in potential at the center $O$ (radius $R$) is:

The work done in moving a $5 \, C$ charge between two points on the surface of a charged conductor is:

If the electric field is in the $Z$-direction, the equipotential surfaces are defined by the equation:

An equipotential surface cannot have a component of electric field parallel to it because:

On an equipotential surface, the potential value at any point $(x, y, z)$ is:

The diagram illustrates three concentric spherical equipotential surfaces $A, B$, and $C$ centered around a point charge $q$. The potentials of these surfaces are $V_A = 60 \text{ V}$, $V_B = 30 \text{ V}$, and $V_C = 20 \text{ V}$. If $d_1$ represents the radial distance between surfaces $A$ and $B$, and $d_2$ represents the radial distance between surfaces $B$ and $C$, what is the ratio $d_1 : d_2$?

A metallic sphere is placed in a uniform electric field. The equipotential surfaces inside the sphere are:

For a dipole, why is the perpendicular bisector an equipotential surface?

The electric potential at the surface of an atomic nucleus ($Z=50$) of radius $9 \times 10^{-15} \text{ m}$ is approximately:

An electron is moved along an equipotential surface of $10 \text{ V}$ from point $A$ to $B$. The work done by the external agent is:

If the potential in a region is $V(x, y, z) = xyz$, then the electric field $\vec{E}$ at $(1, 1, 1)$ is:

In non-polar dielectrics, the center of positive charges and negative charges:

The symbolic representation of a variable capacitor includes:

Two capacitors each of $2\ \mu F$ are connected in series. Their equivalent capacitance is:

Which of the following is another way to express the unit Farad?

A parallel plate capacitor is charged. If the plates are pulled apart, the potential energy of the capacitor:

Two spheres of radii $a$ and $b$ ($a > b$) have the same surface charge density. The ratio of their potentials is:

If the charge on a capacitor is increased by $2\ C$, the energy stored in it increases by $21\%$. The original charge on the capacitor was:

A capacitor of $20 \mu F$ is charged to $500 V$. It is then disconnected and connected to another uncharged capacitor in parallel. If the common potential is $100 V$, the capacitance of the second capacitor is:

The force of attraction between the plates of a parallel plate capacitor is $F$. If a dielectric slab of constant $K$ is inserted while the charge $Q$ is constant, the force becomes:

A capacitor is charged and then the battery is removed. A dielectric slab is then inserted. The work done by the electrostatic forces on the slab is:

The energy stored in a capacitor of $C=2 F$ with $Q=10 C$ is:

What is the energy stored in a $4 \mu F$ capacitor when the potential difference across it is $50 V$?

If the plate area of a parallel plate capacitor is halved while keeping it connected to a battery, the energy stored:

When a capacitor is discharged through a resistor, the stored energy is converted into:

A parallel plate capacitor of capacitance $C$ is connected to a battery of $V$ volts. If the separation between the plates is decreased to half its original value while the battery remains connected, the additional energy supplied by the battery is:

What happens to the energy density of a capacitor if the plate area is doubled while keeping the potential difference and plate separation constant?

An air-filled parallel plate capacitor has capacitance $C$. It is charged to $V$ and then the battery is disconnected. The energy stored is $U$. If the plates are now submerged in an oil of dielectric constant $K=2$, the energy stored becomes:

If the plate separation of a capacitor is decreased by $50\%$ while the battery is connected, the energy stored becomes:

A capacitor of capacitance $C$ is charged to $V$. It is then connected to a battery of $2V$ with similar polarities. The heat produced in the connecting wires is:

A capacitor of $20 \mu F$ is charged to $500 V$. It is then disconnected and connected in parallel with an uncharged $30 \mu F$ capacitor. The common potential is:

When the external electric field applied to an insulator is increased to a very high value, it can detach electrons from the atoms, causing the material to become a conductor. This phenomenon is known as:

In a dielectric, the charges that appear on the surface when an external electric field $\vec{E}$ is applied are not free to move through the material like conduction electrons. These charges are specifically known as:

If the dielectric constant of a medium is $K$, and the force between two charges in vacuum is $F$, what is the force between them in the medium?

In the context of dielectrics, 'isotropic' means that the properties of the material are:

When a dielectric is placed in a non-uniform electric field, the slab will experience:

If we define $C_0$ as the capacitance of an empty capacitor, and $C$ as the capacitance with a dielectric, the ratio $C/C_0$ is:

In a non-polar dielectric, the induced dipole moment is oriented:

Two capacitors of $2 \mu F$ and $4 \mu F$ are connected in parallel. A dielectric of $K=3$ is inserted into the $2 \mu F$ capacitor. The new equivalent capacitance is:

Non-polar dielectrics have:

A parallel plate capacitor is filled with a dielectric whose constant $K$ varies as $K(x) = K_0 e^{x/d}$, where $d$ is the plate separation. The capacitance is:

If a charge is moved from a point of low potential to high potential, the work done by the external agent is:

For a dipole, which point has the maximum absolute value of potential for a given distance $r$?

Can two equipotential surfaces intersect each other?

The electric potential at a point is $10 \, V$. The work done in moving an electron from infinity to that point is:

If the distance between two point charges is doubled, the electrostatic potential energy of the system becomes:

The electric potential at the center of a hemisphere of radius $R$ having uniform surface charge density $\sigma$ is:

Two charges $q_1 = 10 \mu C$ and $q_2 = -10 \mu C$ are placed $5\text{ mm}$ apart. The dipole moment is:

The electric potential at a point distant $r$ from the center of a dipole is $V$. The electric field at that point is $E$. The relation between $V$ and $E$ on the axial line is:

A point charge $q$ is placed at the origin. The potential difference $V_A - V_B$ between points $A(a, 0)$ and $B(a/\sqrt{2}, a/\sqrt{2})$ is:

Three concentric metallic shells $A, B, C$ of radii $a, b, c$ ($a < b < c$) have surface charge densities $\sigma, -\sigma, \sigma$ respectively. The potential of the middle shell $B$ is:

The work done in assembling a system of charges does NOT depend on:

For a system of two like charges, the graph of potential energy $U$ vs distance $r$ is a:

If the potential at a point is $10 V$, the potential energy of a $-2 \mu C$ charge at that point is:

Bringing a test charge from infinity to the center of a dipole along its perpendicular bisector requires work equal to:

The electric potential energy of a system of two point charges is $10\,J$. If the separation between them is tripled, the new potential energy is:

Which of the following is true for a conservative field like the electrostatic field?

A system consists of charges $+q$ and $-q$ at $A$ and $B$. If a third charge $+Q$ is moved from infinity to the midpoint of $AB$, the work done is:

An electron is moving towards another electron. As they get closer, the electrostatic potential energy of the system:

Find the ratio of the potential energy of a system of two charges $q, q$ at distance $r$ to a system where one charge is $q$ and the other is $3q$ at distance $3r$.

Two protons are released from rest when they are $10^{-15} m$ apart. Their kinetic energy when they are very far apart is:

The relation between electric field $E$ and potential $V$ in an external field is:

If we move a charge $q$ between two points with the same external potential, the work done by the external field is:

The potential energy of a dipole is a maximum when the dipole moment is:

What is the potential energy of a system consisting of a single charge $q$ if the external potential $V$ is zero everywhere?

If a charge is released from rest in an external electric field, it moves towards a region of:

Potential energy of a dipole is zero when it is:

For a system of two charges in an external field, if the interaction energy is much smaller than the field energy, the total potential energy is approximately:

A particle of charge $q$ is moved from $(a,0)$ to $(0,a)$ in an electric field $\vec{E} = k(y\hat{i} + x\hat{j})$. The work done by the field is:

A dipole $\vec{p}$ is placed in a field $\vec{E} = E_0 (x/a) \hat{i}$. The potential energy $U$ at $x=0$ (assuming dipole is at $x=0$ and is small of length $\Delta x$) is:

Which of the following is true for a dipole in a uniform electric field?

Earth is a good conductor. Its potential is taken as:

The expression for electrostatic energy density in free space is:

A point charge is placed near an uncharged conducting plate. The plate will:

The electric field inside a conductor is zero. This implies the interior is a:

Three concentric metallic shells $A, B$, and $C$ have radii $a, b$, and $c$ ($a < b < c$) respectively. The shells are given surface charge densities $+\sigma, -\sigma$, and $+\sigma$ respectively. What is the expression for the electrostatic potential $V_B$ on the surface of the middle shell $B$?

Sharper the curvature of a conductor's surface:

Inside a charged hollow conductor, the electric potential is:

For a conductor of arbitrary shape, the potential $V$ on its surface and the electric field $E$ at a point just outside the surface are related such that:

A solid conducting sphere of radius $R$ is placed in a vacuum. If the maximum electric field the air can withstand is $E_{max}$, the maximum charge the sphere can hold is:

A conducting sphere of radius $R$ has a charge $Q$. It is enclosed by a neutral conducting concentric shell of radius $2R$. The potential difference between the sphere and the shell is $V$. If the shell is now given a charge $-3Q$, the new potential difference will be:

Which of the following is a non-polar molecule?

If two identical capacitors are connected first in series and then in parallel, the ratio of equivalent capacitances $C_s / C_p$ is:

Dielectric strength is defined as the maximum:

Formula for energy stored using charge $Q$ and capacitance $C$ is:

The capacitance of a parallel plate capacitor is $12 \mu F$. If the distance between the plates is doubled and the area is halved, then new capacitance will be:

A parallel plate capacitor is connected to a battery. A dielectric slab is then inserted between the plates. Which of the following increases?

Two plates of a parallel plate capacitor are $4 mm$ apart. A slab of dielectric constant 3 and thickness $2 mm$ is introduced. The capacitance:

In a parallel plate capacitor, the potential difference is $V$ and the separation is $d$. If an electron is released from the negative plate, its speed when it reaches the positive plate is:

A parallel plate capacitor is charged to $V$ volts. A dielectric slab is inserted between the plates while it is still connected to the battery. The flux of the electric field through the Gaussian surface enclosing one of the plates:

A parallel plate capacitor of area $A$ has a charge $Q$. The energy required to double the separation from $d$ to $2d$ is:

A dielectric slab is used in a capacitor primarily to:

If the dielectric constant $K$ is increased, the electric field between the plates (for fixed charge $Q$):

The displacement $D$ is related to $E$ and $P$ by:

When a dielectric slab is inserted into a capacitor connected to a battery, the charge on the capacitor $Q$ becomes:

A parallel plate capacitor with plate area $A$ and separation $d$ has a capacitance $C_0$ in air. The space between the plates is filled with three different dielectric slabs as shown in the equivalent circuit configuration. Slabs with dielectric constants $K_1$ and $K_2$ each occupy half the area ($A/2$) and half the thickness ($d/2$). A third slab with dielectric constant $K_3$ occupies the entire area ($A$) and the remaining half thickness ($d/2$). What is the effective capacitance $C$ of this arrangement?

A capacitor $C$ is connected to a battery $V$. A dielectric $K$ is inserted. The charge on the capacitor $Q$ becomes:

When a dielectric slab is inserted into an isolated charged capacitor, the force between the plates:

A parallel plate capacitor is charged and isolated. If a dielectric slab is inserted and it fills the whole volume, the energy density changes from $u_0$ to $u$. The ratio $u/u_0$ is:

If a dielectric slab is inserted into a capacitor while it is being charged by a battery, the total charge $Q$ supplied by the battery is $Q = Q_{initial} + \Delta Q$. The ratio $\Delta Q / Q_{initial}$ is:

In a dielectric-filled capacitor connected to a battery, if the dielectric constant $K$ increases, the energy stored $U$ varies as:

A circuit consists of two $10\, \mu F$ capacitors in parallel, and this group is in series with another $20\, \mu F$ capacitor. The equivalent capacitance is: