Glossary
Batteries
Batteries are devices that use chemical reactions to create and maintain a potential difference between their terminals, acting as a source of electromotive force.
Example:
A car battery uses lead-acid chemistry to provide the 12V needed to start the engine and power the vehicle's electrical systems.
Chemical Processes (Charge Separation)
Certain chemical reactions can separate positive and negative charges, thereby creating an electric potential difference.
Example:
In a voltaic cell, redox reactions drive charge separation across electrodes, building up a potential difference that can power a circuit.
Continuous Charge Distributions (Electric Potential)
The electric potential due to a continuous charge distribution is found by integrating the potential contributions from infinitesimal charge elements (dq) over the entire distribution.
Example:
Determining the electric potential along the axis of a uniformly charged ring requires setting up and solving an integral over the ring's charge elements.
Electric Field Component (from Potential)
Any component of the electric field is equal to the negative spatial rate of change (derivative) of the electric potential in that direction.
Example:
If the potential V(x) is given, taking the negative derivative with respect to x, -dV/dx, directly yields the electric field component E_x.
Electric Field Vectors
Electric field vectors represent the direction and magnitude of the electric force per unit charge at a given point in space.
Example:
Mapping the electric field vectors around a positive point charge shows them pointing radially outward, indicating the direction a positive test charge would accelerate.
Electric Potential
Electric potential is the electric potential energy per unit charge at a specific point in space, representing the 'energy landscape' for charges.
Example:
A high electric potential at a point indicates that a positive test charge placed there would have a large amount of potential energy.
Electric Potential Difference (ΔV)
The electric potential difference is the change in electric potential energy per unit charge when a test charge moves between two points, independent of the path taken.
Example:
When a charge moves from a point of 10V to a point of 2V, the electric potential difference is -8V, indicating a decrease in potential.
Equipotential Lines
Equipotential lines are lines or surfaces that connect points in an electric field that have the same electric potential.
Example:
On a contour map of electric potential, equipotential lines are always drawn perpendicular to the electric field lines, showing regions of constant voltage.
Integrating Field and Displacement (for Potential Difference)
The change in electric potential between two points can be calculated by integrating the negative dot product of the electric field and the displacement vector along any path between the points.
Example:
To find the potential difference across a capacitor, one can perform the integration of the electric field and displacement from one plate to the other.
Linear Charge Density (λ)
Linear charge density is the amount of electric charge distributed uniformly along a unit length of a one-dimensional object, such as a thin rod or wire.
Example:
For a uniformly charged rod of total charge Q and length L, the linear charge density is simply Q/L, used when calculating potential or field from continuous distributions.
Permittivity of Free Space (ε₀)
The permittivity of free space is a fundamental physical constant representing the ability of a vacuum to permit electric field lines.
Example:
The constant ε₀ appears in Coulomb's Law and formulas for electric potential, indicating how electric forces and fields behave in a vacuum.
Point Charge (Electric Potential)
The electric potential due to a single point charge is inversely proportional to the distance from the charge and directly proportional to the charge's magnitude.
Example:
Calculating the electric potential at a specific distance from a proton helps determine the energy required to bring another charged particle close to it.
Superposition Principle (for Electric Potential)
The total electric potential at a point due to multiple point charges is the scalar sum of the potentials created by each individual charge.
Example:
To find the electric potential at the center of a square with charges at each corner, you simply add up the potential contributions from each of the four charges.
Volts (V)
Volts are the SI unit for electric potential and electric potential difference, defined as one joule per coulomb (J/C).
Example:
A standard AA battery provides a voltage of 1.5 V, meaning it can supply 1.5 joules of energy for every coulomb of charge that moves through it.