Suppose that F is an inverse square force field, that is,

for some constant c, where r = x i + y j + z k.

(a) Find the work done by F in moving an object from a point P₁ along a path to a point P₂ in terms of the distances d1 and d2 from these points to the origin.

(b) An example of an inverse square field is the gravitational field F = −(mMG)r/|r|³. Use part (a) to find the work done by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52 × 10⁸ km from the sun) to perihelion (at a minimum distance of 1.47 × 10⁸ km). (Use the values m − 5.97 × 10²⁴ kg, M = 1.99 × 10³⁰ kg, and G = 6.67 × 10⁻¹¹ N∙m²/kg².)

(c) Another example of an inverse square field is the electric force field F = εqQr/|r|³. Suppose that an electron with a charge of −1.6 × 10⁻¹⁹ C is located at the origin. A positive unit charge is positioned a distance 10212 m from the electron and moves to a position half that distance from the electron. Use part (a) to find the work done by the electric force field. (Use the value ε = 8.985 × 10⁹.)

Transcribed Image Text:

cr F(r) 13 r