AP Physics C: E&M Unit 8 Formulas

Formula(s) for electric field?

\overrightarrow{E} = \frac{\overrightarrow{F}_e}{q_0} = k_e\frac{q}{r_0²}\hat{r}

What sign is the test charge always assumed to be?

positive

Formula for electric force for point charges only?

\overrightarrow{F}_e = q\overrightarrow{E}

q>0, what direction are the force and field in?

same direction

q<0, what direction are the force and field in?

opposite directions

For a positive particle, how are the field lines oriented?

radially outward

For a negative particle, how are the field lines oriented?

radially inward

Two equal yet oppositely charged particles are at radius r. What are some properties of the field?

• Field is strongest in the middle of the two charges

• Lines from + go to infinity

  • Lines to - start at infinity and terminate at the charge

Where do field lines start and terminate?

start at + and terminate at -

Two equal charges with same sign are at a distance r. What are the properties of the field?

• Field is 0 at the center

• Lines end infinitely far away

  • Far away, the field is roughly like a charge of 2q

Two unequal and opposite charges are at distance r. What are the properties of the field?

• x lines leave the greater charge for every y of the opposite charge

  • Far away, the field is roughly that of a single charge

Uniform fields have constant _____?

acceleration

Integral definition for electric fields?

\overrightarrow{E} = k\int \frac{1}{r²}\hat{r}dq

Linear charge density?

\lambda = \frac{q}{L}

Surface charge density?

\sigma = \frac{q}{A}

Volumetric charge density?

\rho = \frac{q}{V}

Electric fields are extremely long distances (linear density)?

\overrightarrow{E}_x = \frac{2k\lambda}{D}

Electric fields for points perpendicular to a line of charge?

\overrightarrow{E}_x = \frac{kQ}{D\sqrt{D²+(\frac{L}{2})²}}

Perpendicular electric fields for full rings of charge at a distance D from the center axis?

0

Parallel electric fields for charged rings at a distance D on the center axis?

\overrightarrow{E} = \frac{kDQ}{(R²+D²)^{\frac{3}{2}}}

Electric fields for arcs of charge?

\overrightarrow{E} = k \cdot \frac{\lambda}{R} \int_{-\alpha}^{\alpha} cos(\theta)d\theta \hat{i}

Gauss’s Law formula?

\Phi_E = \oint \overrightarrow{E} \cdot dA = E \cdot Acos(\phi) = \frac{Q_{enc}}{\epsilon_0}

When is \frac{Q_{enc}}{\epsilon_0} used for Gauss’s law?

Enclosed surfaces

When is the dot product E \cdot Acos(\phi) used for Gauss’s Law?

non-enclosed surfaces

At what angle is flux at its maximum?

when \phi = 0

At what angle is flux at a minimum?

when \phi = 90

Does changing the radius of a gaussian surface change the flux?

no

Does changing the shape of a gaussian surface change the flux?

no

Does changing the location of the interior charge of a gaussian surface change the flux?

no

Does changing the enclosed charge value of a gaussian surface change the flux?

yes

What are some flux/field properties of conductive sheets?

• The field is 0 inside the material

• Creates charge density on both sides

What are some flux/field properties of insulating sheets?

• Field is a non-zero value inside the material

  • Charging makes a charge density on only one side

Field equation for conductive sheets?

\overrightarrow{E} = \frac{\sigma}{\epsilon_0}

Field equation for insulating sheets?

\overrightarrow{E} = \frac{\sigma}{2\epsilon_0}