Electrostatic Potential and Capacitance

These flashcards cover key concepts and definitions related to electrostatic potential and capacitance based on the lecture notes.

What is potential energy in the context of conservative forces?

Potential energy is the energy stored when an external force does work against a conservative force, like gravitational or spring forces.

What happens to potential energy when an external force is removed?

The body moves, gaining kinetic energy and losing an equal amount of potential energy.

What defines conservative forces?

Forces for which the work done in moving a charge depends only on the initial and final positions, not the path taken.

Give examples of conservative forces.

Gravitational force, spring force, and Coulomb force.

What is electrostatic potential energy?

The work done in bringing a test charge from infinity to a point in an electrostatic field.

How is work done by external forces defined in electrostatics?

Work done is defined as the negative of the work done by electric forces.

What is the formula for potential energy difference between two points R and P?

ΔU = UP - UR = - WRP.

Why is the work done by an electrostatic field considered negative?

Because the displacement is opposite to the direction of the electric force.

What does the electrostatic potential represent?

The work done per unit charge in bringing a charge from infinity to a specified point.

What is the expression for electric potential due to a point charge Q?

V(r) = (1 / (4πε₀)) * (Q / r).

What is the relationship between electric field and potential?

Electric field is equal to the negative gradient of electric potential.

What are equipotential surfaces?

Surfaces where the potential is constant throughout.

What is the significance of potential energy difference?

It is the physically meaningful quantity, while the absolute potential energy is arbitrary.

Define capacitance.

Capacitance (C) is defined as the ratio of charge (Q) stored on a conductor to the potential difference (V) across it.

What is the SI unit of capacitance?

Farad (F), which is equal to one coulomb per volt (C/V).

Describe a parallel plate capacitor's characteristics.

It consists of two large parallel plates separated by a small distance, and its capacitance depends on area (A) and separation (d).

What does the presence of a dielectric do to capacitance?

It increases the capacitance by a factor known as the dielectric constant (K).

Express the capacitance of a parallel plate capacitor with a dielectric.

C = (Kε₀A) / d.

What is the electric field inside a conductor in electrostatic equilibrium?

The electric field is zero inside a conductor.

What is electrostatic shielding?

The phenomenon where the electric field inside a cavity in a conductor is zero, shielding it from external fields.

Calculate the energy stored in a capacitor.

The energy U is given by U = 1/2 CV² = 1/2 QV.

What is the energy density of an electric field?

Energy density u is given by u = (1/2)ε₀E².

What is the potential energy of a dipole in a uniform electric field?

The potential energy U is given by U = -p·E, where p is the dipole moment and E is the electric field.

Can work done by the electrostatic field be negative?

Yes, the work done can be negative if it is done against the electric field.

Explain the superposition principle for electric potential.

The total potential at a point is the algebraic sum of potentials due to individual charges.

What happens to potential energy when two point charges are brought together?

The potential energy is determined by the work done to assemble the configuration of the charges.

Define electrical potential at a point.

Electrical potential is the work done per unit charge in bringing a charge from infinity to that point.

What happens when capacitors are connected in series?

The total capacitance is given by 1/C = 1/C1 + 1/C2 + … for n capacitors.

What happens when capacitors are connected in parallel?

The total capacitance is the sum of individual capacitances: C = C1 + C2 + ….

What is the impact of external fields on the energy of a capacitor?

The energy stored in a capacitor can change depending on the external field and configuration.

What occurs during the transient period after connecting two capacitors?

A transient current flows between the two capacitors, leading to energy loss in the form of heat when they equalize potential.

What is the primary characteristic of a dielectric in an electric field?

It develops induced dipole moments that partially oppose the external field.

What is the relationship between the electric potential and the distance from the center of a conducting sphere?

The electric potential is constant inside a conducting sphere and decreases as 1/r outside.

What value does the electric potential have at the surface of a conducting sphere?

The electric potential at the surface of a conducting sphere is equal to the potential due to the total charge divided by the radius.

How does the electric potential behave inside a hollow conducting sphere?

Inside a hollow conducting sphere, the electric potential is constant and equal to the potential on the surface.

When observing a charged solid sphere, what happens to the electric potential at a point outside the sphere?

At a point outside a charged solid sphere, the electric potential behaves as if all the charge were concentrated at the center.

What formula is used to calculate the electric potential (V) due to a point charge (Q) at a distance (r)?

The formula is V = k * Q / r, where k is Coulomb's constant.

What is the formula for the energy (U) stored in a capacitor?

U = 1/2 CV², where C is the capacitance and V is the voltage across the capacitor.

How does the energy stored in a capacitor change when the charge is doubled while keeping capacitance constant?

The energy is quadrupled as it is proportional to the square of the voltage (U = 1/2 C(2V)² = 2CV²).

What effect does a dielectric material have on the capacitance of a capacitor?

A dielectric material increases the capacitance by a factor equal to its dielectric constant (κ).

If a capacitor with a dielectric is charged to a potential difference and then isolated (not connected to a battery), what happens to the energy stored when the dielectric is inserted?

The energy decreases because the voltage across the capacitor decreases while the charge remains constant.

What happens to the energy stored in a capacitor if the voltage is halved?

The energy stored is reduced to one-quarter of its original value, since U = 1/2 CV².