Physics Ch.1 Electric Charges and Fields

Comprehensive practice questions covering the fundamentals of electrostatics, including charge properties, Coulomb's Law, electric fields, dipoles, and Gauss's Law.

What is the definition of the term 'static' in the context of physics?

Static refers to anything that does not move or change with time.

What does the branch of physics known as electrostatics study?

Electrostatics deals with the study of forces, fields, and potentials arising from static charges.

To whom is the historical discovery attributed that amber rubbed with wool or silk attracts light objects?

The credit goes to Thales of Miletus, Greece, around $600\,BC$.

What is the Greek origin of the word 'electricity'?

It is coined from the Greek word 'elektron', meaning amber.

What are the two fundamental rules governing the interaction between charges?

(i) Like charges repel and (ii) unlike charges attract each other.

What is the specific property that differentiates the two kinds of electric charges?

The property is called the polarity of charge.

Which scientist named the two types of charges positive and negative?

The American scientist Benjamin Franklin.

What simple apparatus is used to detect the presence of charge on a body?

The gold-leaf electroscope, which consists of a vertical metal rod with two thin gold leaves that diverge when charged.

In electricity, how does a neutral body become positively charged in terms of electron transfer?

A body becomes positively charged by losing some of its electrons.

Define the term 'conductors' and provide examples.

Conductors are substances that allow electricity to pass through them easily; examples include metals, human and animal bodies, and earth.

Define the term 'insulators' and provide examples.

Insulators are substances that offer high resistance to the passage of electricity; examples include glass, porcelain, plastic, nylon, and wood.

What is the principle of 'Additivity of charges'?

If a system contains n charges $q_1, q_2, q_3, \dots, q_n$, the total charge of the system is the algebraic sum: $q_1 + q_2 + q_3 + \dots + q_n$.

What does the law of conservation of charge state?

The total charge of an isolated system is always conserved; charges may be redistributed but not created or destroyed.

What is the mathematical expression for the quantisation of charge?

$q = ne$, where $n$ is any integer (positive or negative) and $e$ is the basic unit of charge.

What is the value of the basic unit of charge $e$ in SI units?

$e = 1.602192 \times 10^{-19}\,C$.

State Coulomb's Law for the magnitude of force between two point charges in vacuum.

$F = k \frac{|q_1 q_2|}{r^2}$, where $k = \frac{1}{4\pi\varepsilon_0}$.

What is the approximate value of the constant $k$ in SI units for Coulomb's Law?

$k \approx 9 \times 10^9\,N\,m^2\,C^{-2}$.

What is the value and definition of $\varepsilon_0$?

$\varepsilon_0$ is the permittivity of free space, and its value is $8.854 \times 10^{-12}\,C^2\,N^{-1}m^{-2}$.

How is the electric field $\mathbf{E}$ defined operationally at a point in space?

$\mathbf{E} = \lim_{q \to 0} \frac{\mathbf{F}}{q}$, where $\mathbf{F}$ is the force experienced by a small test charge $q$.

What is the SI unit of electric field?

Newtons per Coulomb ($N/C$) or Volts per meter ($V/m$).

List four general properties of electric field lines.

(1) They start at positive charges and end at negative charges. (2) In charge-free regions, they are continuous without breaks. (3) Two lines never cross. (4) They do not form closed loops.

How is electric flux $\Delta \phi$ through an area element $\Delta S$ defined?

$\Delta \phi = \mathbf{E} \cdot \Delta \mathbf{S} = E \Delta S \cos(\theta)$, where $\theta$ is the angle between $\mathbf{E}$ and the normal to the area element.

What is an electric dipole?

A pair of equal and opposite point charges $q$ and $-q$, separated by a distance $2a$.

What is the formula for the dipole moment vector $\mathbf{p}$?

$\mathbf{p} = q \times 2a\,\mathbf{\hat{p}}$, directed from $-q$ to $+q$.

How does the magnitude of the electric field of a dipole vary with distance $r$ at large distances?

It falls off as $\frac{1}{r^3}$.

What torque $\mathbf{\tau}$ is experienced by a dipole $\mathbf{p}$ in a uniform external field $\mathbf{E}$?

$\mathbf{\tau} = \mathbf{p} \times \mathbf{E}$.

Define surface charge density $\sigma$.

$\sigma = \frac{\Delta Q}{\Delta S}$, with units of $C/m^2$.

State Gauss's Law mathematically.

$\phi = \frac{q}{\varepsilon_0}$, where $\phi$ is the total electric flux through a closed surface and $q$ is the total charge enclosed.

What is the electric field inside a uniformly charged thin spherical shell?

$E = 0$ for $r < R$, where $R$ is the radius of the shell.

What is the electric field due to an infinitely long thin straight wire of uniform linear charge density $\lambda$?

$E = \frac{\lambda}{2\pi\varepsilon_0 r}$, where $r$ is the perpendicular distance from the wire.