Module 10- Fields

Module 10- Fields

1. 10.2 Fields at Work

   • Gravitational Potential Energy
     • Local formula for gravitational potential energy=Ep=mg
     • change in Vg=change in Ep/m so vg=-GM/r
     • Scalar value
     • Gravitational potential gradient is the change in gravitational potential per unit distance
       • GPG=change in Vg/change in r
   • Gravitational Equipotentials
     • For a point mass the gravitational field lines point inwards
     • The gravitational field lines are perpendicular to the equipotential surfaces
   • Escape and Orbit Speed
     • Vesc=Sqrt(2GM/R)
     • Total energy of an orbiting satellite=(1/2)mv^2-GMm/r
       • E=Ek+Ep
     • Speed of an orbiting satellite- vorbit=sqrt(GM/r)
     • Total energy of an orbiting satellite 2= -GMm/2r
   • Electrostatic Potential Energy
     • Electrostatic potential energy is the word done by the electrostatic field in bringing a small charge from infinity to that point
       • Ve=kq/r
     • The potential gradient is -change in Ve/change in r

2. 10.1 Describing Points

   • Conservative Forces
     • We call any force that does work independent of path a conservative force
     • Only conservative forces have associated potential energy functions
     • Gravitational force is a conservative force
     • Potential Energy Function: change in Ep=-w=Fdcos(theta). Where F is a conservative force
       • Ep=kQq/r
     • Fe=kQq/r^2
     • Fg=-GMm/r^2
   • Force Fields
     • Charges and masses are imagined as capable of warping the space around them due to their presence
     • Negative charge have arrows going towards them
     • Positive charges have arrows going away from them
   • Potential Difference
     • Work is done for the electric and gravitational forces as they experience charges
       • change in Ve=W/q
       • Change in Vg=W/m
   • Equipotential Surfaces
     • Each line represents a plane of constant potential, an equipotential surface
     • When mass is moved along an equipotential surface, no work is done by the gravitational field.
     • Field lines are always perpendicular to the equipotential surfaces