# Wright State University Lake Campus/2017-9/Phy2410/Brief equations T4

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#### 00-Mathematics for this course[edit]

Measured in radians, defines angle (in radians). The circumference of a circle is and the circle's area is is its area. The surface area of a sphere is and sphere's volume is

#### 01-Introduction[edit]

- Earth's gravitational acceleration = g ≈ 9.8m/s
^{2}. Speed of light = c ≈ 3×10^{8}m/s. The electron has charge, e ≈ 1.6 × 10^{−19}C and mass ≈ 9.11 × 10^{-31}kg. 1eV = 1.602 × 10^{-19}J is a unit of energy, defined as the work associated with moving one electron through a potential difference of one volt. - ≈ 8.987× 10
^{9}N·m²·C^{−2}is a fundamental**constant of electricity**; also ≈ 8.854 × 10^{−12}F·m^{−1}is the vacuum permittivity or the electric constant. - = 4π × 10
^{−7}NA ≈ 1.257 × 10^{−6}N A (magnetic permeability) is the**fundamental constant of magnetism**: .

#### 18-Electric charge and field[edit]

- is Coulomb's law for the force between two charged particles separated by a distance r: k
_{e}≈8.987×10^{9}N·m²·C^{−2}, and ε_{0}≈8.854×10^{−12}F·m^{−1}. - is the electric force on a "test charge", q.

Consider a collection of particles of charge , located at points (called *source points*), the electric field at (called the *field point*) is:

- is the electric field at the field point, , due to point charges at the source points, , and points from source points to the field point.

is the electric field due to distributed charge, where , and denote *linear*, *surface*, and *volume* density (or *charge density*), respectively. Line element:.

#### 19-Electric Potential and Electric Field[edit]

- is the potential energy of a particle of charge, q, in the presence of an electric potential V.
- (measured in Volts) is the variation in electric potential as one moves through an electric field . If the field is not univorm, then
- is the (equal and opposite) charge on the two terminals of a capacitor of capicitance, C, that has a voltage drop, V, across the two terminals.
- is the capacitance of a parallel plate capacitor with surface area, A, and plate separation, d. This formula is valid only in the limit that d
^{2}/A vanishes. If a dielectric is between the plates, then ε>ε_{0}≈ 8.85 × 10^{−12}due to shielding of the applied electric field by dielectric polarization effects. - is the energy stored in a capacitor.

- is Gauss's law for the surface integral of the electric field over
*any*closed surface, and is the total charge inside that surface.

#### 20-Electric Current, Resistance, and Ohm's Law[edit]

- defines the electric current. is Ohm's Law relating I, and resistance, R, to the difference in voltage, V, between the terminals. is the power dissipated as current flows through a resistor. Power is the rate at which energy is transformed.