Fields

Fields

1. Gravitational fields

   • Field Lines - If a small objects is in free fall due to gravity, the path it follows is called a field line/line of force.
     • Radial Field Lines
       • Radial field lines are always directed towards center of mass.
         • Further radial field lines are spread out, the weaker the force (vice versa). (Within a small distance, assume uniform field)
     • Uniform Field Lines
       • Gravitational field strength is same in direction and magnitude everywhere in the field. They're parallel and equally spaced (equal force).
     • G Field Strength: g = F/m
   • Weight of object = force of gravity on a mass

2. Gravitational Potential

   • Gravitational Potential Energy = Energy of an object due to its position in a gravitational field. (Jkg-1)
     • 0 GPE is at infinity - (objects so far away, force on it is negligible)
     • A rockets needs to increase its GPE to 0 to escape the planets field. At surface its GPE is negative, needs to do work to reach 0.
     • GPE at a point = The work done per unit mass to move a small object from infinity to that point. V = w/m
   • Potential Gradients
     • Equipotentials = surfaces of constant potential.
       • No work needs to be done to move across an equipotential surface.
       • Example: Contour lines on a map are equipotentials, the contour lines join at equal height above sea level. Hillwalkers following a contour line has constant potential energy. If a hillwalker slips off the contour lines their GPE might fall dramatically.
         • Gravitational field over a small region is uniform as equipotentials are parallel to the surface.
         • Gravitational field strength is negative of the potential gradient. g = - change in potential (v) / over a small distance (r)
       • Further the equipotentials are away from the surface, the field becomes weaker = Gain of GPE from surface per meter height becomes less.
     • Potential gradient at a point in a field = change of potential per meter at the same point. Potential Gradient = change of potential (v) / over a small distance (r)
       • Like contour gradients on a map. The closer the contours on a map, the steeper the hill = The closer the equipotentials are, the greater the potential gradient, stronger the field.
         • Where equipotentials show equal changes of potential for equal changes of spacings, potential gradient is constant.
           • Direction of lines of force of gravitational field are always perpendicular to equipotentials.

3. Newton's Law of Gravitation

   • Newton realised gravity is universal
   • Any two masses exert a force of attraction

4. Planetry

   • Law of gravitation used to determine the grav. field strength
     • Newton showed that the field of sphere mass is concentrated at the centre.
       • Newton's law of gravitation: F=Gmm/r2

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