Physics Exam Study Guide: Electric Fields, Flux, Capacitance, and Current

SI Prefixes

Introduction to SI Prefixes

SI prefixes are used to denote decimal multiples and submultiples of units in the International System of Units (SI). They are essential for expressing measurements in physics, especially when dealing with very large or very small quantities.

Prefix	Symbol	Factor	Prefix	Symbol	Factor
femto	f	10-15	hecto	h	102
pico	p	10-12	kilo	k	103
nano	n	10-9	mega	M	106
micro	μ	10-6	giga	G	109
milli	m	10-3	tera	T	1012
centi	c	10-2	peta	P	1015

Electric Fields and Flux

Electric Field Lines and Flux

The electric field is a vector field that describes the force per unit charge exerted on a test charge at any point in space. Electric flux quantifies the number of electric field lines passing through a given surface.

• Electric Field (E): The force per unit charge, given by $\vec{E} = \frac{\vec{F}}{q}$.

• Electric Flux (Φ): The total number of electric field lines passing through a surface, $\Phi_E = \int \vec{E} \cdot d\vec{A}$.

• Gauss's Law: Relates the electric flux through a closed surface to the charge enclosed, $\Phi_E = \frac{Q_{\text{enc}}}{\varepsilon_0}$.

• Direction of Electric Field: Points away from positive charges and toward negative charges.

Applications and Examples

• Dipole Field: The field lines emerge from the positive charge and terminate at the negative charge. The flux through a closed surface enclosing both charges is zero.

• Flux through a Cylinder: For a cylinder with equal and opposite charges at each end, the net flux is zero.

• Flux through a Cube: If the net charge inside is $q$, the total flux is $\frac{q}{\varepsilon_0}$.

Conductors and Electric Fields

Properties of Conductors

Conductors allow free movement of electric charge. In electrostatic equilibrium, the electric field inside a conductor is zero, and any excess charge resides on the surface.

• Surface Charge Density (σ): $\sigma = \frac{Q}{A}$, where $Q$ is the charge and $A$ is the area.

• Electric Field at Surface: $E = \frac{\sigma}{\varepsilon_0}$ just outside the surface.

• Potential of Conductors: All points on a conductor in electrostatic equilibrium are at the same potential.

Examples

• Concentric Spheres: The electric field between spheres can be found using Gauss's Law.

• Surface Charge Density Calculation: For a sphere of radius $r$ and charge $Q$, $\sigma = \frac{Q}{4\pi r^2}$.

Capacitance and Capacitors

Capacitance Basics

Capacitance is the ability of a system to store electric charge. It is defined as the ratio of the charge stored to the potential difference across the plates.

• Capacitance (C): $C = \frac{Q}{V}$

• Parallel Plate Capacitor: $C = \varepsilon_0 \frac{A}{d}$, where $A$ is the area and $d$ is the separation.

• Energy Stored: $U = \frac{1}{2}CV^2$

• Series and Parallel Combinations:

  • Series: $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$

  • Parallel: $C_{\text{eq}} = C_1 + C_2 + \cdots$

Examples

• Two Identical Capacitors in Series: $C_{\text{eq}} = \frac{C}{2}$

• Two Identical Capacitors in Parallel: $C_{\text{eq}} = 2C$

Electric Potential and Potential Energy

Electric Potential

Electric potential is the work done per unit charge in bringing a test charge from infinity to a point in space.

• Potential due to Point Charge: $V = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r}$

• Potential Energy of System: For two point charges, $U = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r}$

Examples

• Potential at Center of Ring of Charges: Sum the contributions from each charge.

• Potential Energy of Multiple Charges: Add pairwise potential energies.

Current, Drift Speed, and Resistance

Current and Drift Speed

Electric current is the flow of electric charge. Drift speed is the average velocity of charge carriers in a conductor.

• Current Density (J): $J = \frac{I}{A}$

• Drift Speed (v_d): $v_d = \frac{I}{nAe}$, where $n$ is the number density of charge carriers, $A$ is cross-sectional area, and $e$ is the elementary charge.

• Ohm's Law: $V = IR$

• Resistance: $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is length, and $A$ is area.

Examples

• Comparing Drift Speeds: For wires of different materials, drift speed depends on carrier density and current.

• Current Density of Protons Near Earth: $J = n e v$, where $n$ is number density, $e$ is charge, and $v$ is velocity.

Summary Table: SI Prefixes

The following table summarizes the SI prefixes used in physics:

Prefix	Symbol	Factor
femto	f	10-15
pico	p	10-12
nano	n	10-9
micro	μ	10-6
milli	m	10-3
centi	c	10-2
hecto	h	102
kilo	k	103
mega	M	106
giga	G	109
tera	T	1012
peta	P	1015

Additional info:

• All topics above are based on the exam questions and SI prefix table provided in the file.

• Examples and equations have been expanded for academic completeness.