10.1 Describing Fields

• Gravitational Fields

  • Specific energy and energy density are vital for quantifying the energy released during combustion.

  • A gravitational field is a region where a small test mass experiences a force due to another mass. 

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• Electrostatic Fields

  • An electrostatic field is a space where a small positive test charge experiences a force per unit charge.

• Electric Potential and Gravitational Potential

  • Electric Potential

    • Given by electric potential difference (voltage).

    • Or v = w / q_moved

  • Gravitational Potential

    • Gravitational potential due to mass M is the work done per unit mass required to move a test mass from infinity to a point P.

    • Gravitational potential is always negative.

    • The potential at infinity is zero.

    • To find potential due to multiple masses, add potentials due to individual masses.

• Field Lines

  • Field lines show the path a test particle would take in a force field, revealing its direction and strength.

• Equipotential Surfaces

  • Points with the same gravitational potential form equipotential surfaces.

  • Field lines are normal to equipotential surfaces.

  • Density of field lines is proportional to field strength.

  • Near Earth's surface, gravitational field strength is relatively constant with height.

10.2 Fields at Work

• Potential and Potential Energy

  • Electric Potential Energy

    • Given by Coulomb's constant (k), fixed charge (Q), test charge (q), and radius (r).

    • Defined as the capacity for doing work by a change in position of the positive test charge.

  • Gravitational Potential Energy

    • Given by mass M, mass m, and radius (r).

    • Work done required to move an object from infinity to a point P.

    • Gravitational potential energy is always negative.

• Potential Gradient

  • Gravitational potential gradient is ΔV/Δr, related to gravitational field strength (g) by g = -ΔV/Δr = GM/r².

  • It represents the slope of a graph plotting gravitational potential against distance from the mass.

• Potential Difference

  • Defined as the work done by moving a positive test charge between two points in an electric field.

  • Voltage across an electrical component is required for current flow.

  • Cells or batteries provide the necessary potential difference.

• Escape Speed

  • The escape speed of a planet is given by G(M/R)^0.5.

  • Escape speed is the minimum speed needed for an object to reach infinity from a planet's surface.

  • Objects launched at or above escape speed won’t return due to gravity.

• Orbital Motion, Orbital Speed, and Orbital Energy

  • Orbital Motion

    • Gravitation provides the centripetal force for orbital motion.

    • Orbital period is proportional to the average radius by Kepler’s third law.

  • Orbital Speed

    • Given by (GM/r)^0.5, where G is the gravitational constant, M is the mass, and r is the radius.

  • Orbital Energy

    • Kinetic energy, gravitational potential energy, and total energy are defined for an orbiting satellite.

• Forces and Inverse-Square Law Behavior

  • Inverse-Square Law Graphical Representation

    • Graphical representation of inverse-square law behavior for gravitational and electric fields.

  • Gravitational Field

    • Graphical representation of the gravitational field in accordance with the inverse-square law.

  • Electric Field

    • Graphical representation of the electric field in accordance with the inverse-square law.