Glossary
Density (ρ)
A scalar quantity representing the mass per unit volume of a substance, indicating how much matter is packed into a given space.
Example:
Wood floats on water because its density is less than that of water.
Electric Field (E)
A vector field that describes the force exerted on a positive test charge at any given point in space due to other charges.
Example:
Around a positively charged sphere, the electric field lines point radially outward, indicating the direction a positive charge would be pushed.
Electric Field Lines
Imaginary lines used to visualize an electric field, pointing away from positive charges and towards negative charges, with their density indicating field strength.
Example:
When sketching the electric field lines between a positive and negative charge, they curve from the positive charge and terminate on the negative charge, never crossing.
Electric Potential (V)
A scalar field that represents the amount of electric potential energy per unit charge at a given point in an electric field.
Example:
A battery creates a difference in electric potential between its terminals, driving current through a circuit.
Equipotential Lines
Lines or surfaces in a scalar field (like electric potential) where all points have the same potential value, meaning no work is done moving along them.
Example:
On a contour map, each equipotential line connects points of equal elevation, so walking along one means you are neither going uphill nor downhill.
Gradient
A vector operation that indicates the direction and rate of the greatest increase of a scalar field, connecting scalar and vector fields.
Example:
If you are on a hill, the gradient of the elevation field points in the direction of the steepest uphill slope.
Graphical Representation of Vectors
Vectors are visually depicted as arrows, where the arrow's length signifies the vector's magnitude and its orientation indicates the vector's direction.
Example:
When drawing the force exerted by a spring, a longer arrow shows a stronger force, and the arrow's direction shows where the force is pushing or pulling.
Gravitational Field (g)
A vector field that describes the gravitational force per unit mass at any point in space, typically pointing towards the source of gravity.
Example:
Near Earth's surface, the gravitational field is approximately uniform and points downwards, causing objects to fall.
Magnetic Field (B)
A vector field that describes the influence of magnetic forces on moving electric charges, electric currents, and magnetic materials.
Example:
Iron filings sprinkled around a bar magnet align themselves along the magnetic field lines, revealing the invisible force pattern.
Pressure (P)
A scalar quantity defined as force per unit area exerted perpendicularly on a surface, typically in a fluid.
Example:
The pressure inside a bicycle tire is higher than atmospheric pressure, allowing it to support weight.
Scalar Fields
A region of space where a scalar quantity is assigned to every point, illustrating how that quantity varies across the area without direction.
Example:
A topographic map uses contour lines to represent a scalar field of elevation, showing how the height changes across a landscape.
Scalar Quantities
Physical quantities described solely by their magnitude (size) and units, without any associated direction.
Example:
The temperature of a room is 22°C, indicating only how hot it is, not a direction.
Temperature (T)
A scalar quantity representing the degree of hotness or coldness of a substance, related to the average kinetic energy of its particles.
Example:
The temperature inside a refrigerator is kept low to preserve food, indicating a specific thermal state without direction.
Vector Fields
A region of space where a vector quantity is assigned to every point, illustrating how that quantity varies across the area.
Example:
A weather map showing wind velocity across a continent uses arrows at different locations to represent both the speed and direction of the wind.
Vector Quantities
Physical quantities described by both magnitude (size) and a specific direction.
Example:
A car moving at 60 km/h North has a vector quantity of velocity, specifying both speed and direction.