Electrostatics and Electric Fields (4C) - MCAT Chemical and Physical Foundations of Biological Systems

Radially inward toward the charge. The field points in the direction a positive test charge would be forced, attracting to a negative source.

$\Delta V = \frac{\Delta U}{q}$. Potential difference measures the change in potential energy per unit charge moved between points.

$W_{\text{field}} = -q\Delta V$. For conservative fields, work by the field equals the negative change in potential energy.

$E_x = -\frac{dV}{dx}$. The electric field component is the negative rate of change of potential with position.

$E = \frac{\Delta V}{d}$. In uniform fields, the field strength equals the potential gradient across the plate separation.

From the $+$ plate toward the $-$ plate. The field points from higher to lower potential, consistent with force on positive charges.

Field lines intersect equipotentials at $90^\circ$. The field direction is perpendicular to surfaces of constant potential, following the gradient.

$V = k\frac{Q}{r}$. The potential is the work per unit charge to bring a test charge from infinity to that point.

$e = 1.60 \times 10^{-19}\ \text{C}$. This magnitude represents the fundamental unit of charge carried by a proton or electron.

Coulomb (C). The coulomb quantifies electric charge in the SI system as the charge transported by a constant current of one ampere in one second.

$k = \frac{1}{4\pi\varepsilon_0}$. Coulomb's constant relates to the vacuum permittivity through this expression in electrostatics.

$F = k\frac{|q_1 q_2|}{r^2}$. The law states that the force is proportional to the product of charges and inversely proportional to the square of the distance.

$\text{N/C}$ (equivalently $\text{V/m}$). The unit derives from force per unit charge or equivalently potential difference per unit distance.

$k \approx 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$. This value is derived from fundamental constants and used in Coulomb's law for vacuum.

$F \to \frac{F}{4}$. Coulomb's law's inverse square dependence on distance quarters the force when distance doubles.

$E_{\text{net}} = 0$. At the midpoint, fields from identical charges are equal in magnitude but opposite in direction, canceling out.

Toward the $-Q$ charge (from $+Q$ to $-Q$). Fields from opposite charges at the midpoint add constructively, pointing towards the negative charge.

$\Delta U < 0$. Moving along the field decreases potential for positive charges, reducing potential energy.

Radially outward from the charge. The field direction indicates the force on a positive test charge, repelling from a positive source.

$E = k\frac{|Q|}{r^2}$. The expression comes from dividing the Coulomb force on a test charge by its magnitude.

$\vec{E}_{\text{net}} = \sum_i \vec{E}_i$. Electric fields obey vector addition, allowing the total field to be the sum of individual contributions.

$U = k\frac{q_1 q_2}{r}$. This represents the work to assemble the charges from infinite separation, positive for like charges.

Volt (V) = $\text{J/C}$. The volt equals one joule of energy per coulomb of charge.

$E \to \frac{E}{9}$. The inverse square law reduces the field to one-ninth when distance increases by a factor of three.