86.4 The gravitational field and Gauss's law for thethe gravitational field Nonuniform vector field dd=p·dS D=[4s= The differential flux dop of the gravitational field vector through the differential area ds is defined to be the do=g ds scalar product of8 with ds gdS cos T /2=0 do=gds=gdS cos 8= gds cos0=gds gds cos丌=-gdS 56.4 The gravitational field and Gauss's law The total flux through the area s or a closed surface s: rdo= a ①=5d@=5gds Choose the outward direction as the direction of the surface element ds for a closed surface Example 2: find the flux of the local gravitational field near the surface of the earth through each of the five surfaces of the inclined plane and the total flux of the entire closed surface 1818 §6.4 The gravitational field and Gauss’s law for the the gravitational field The differential flux dΦ of the gravitational field vector through the differential area dS is defined to be the scalar product of with . g r S r g d r g S r v dΦ = ⋅d ⎪ ⎩ ⎪ ⎨ ⎧ = − = = = ⋅ = = g S g S g S g S g S g S g S d cos d d cos0 d d cos 2 0 d d d cos π π Φ θ r v S r d g r θ v S r r dΦ = ⋅d ∫ ∫ = ⋅ = ⋅ area S area S dS dS r r r r Φ v Φ v S1 S 2 Nonuniform vector field §6.4 The gravitational field and Gauss’s law for the the gravitational field ∫ ∫ ∫ ∫ = = ⋅ = = ⋅ S S g S g S r r r r d d d d S S Φ Φ Φ Φ The total flux through the area S or a closed surface S: Choose the outward direction as the direction of the surface element dS for a closed surface. Example 2: find the flux of the local gravitational field near the surface of the earth through each of the five surfaces of the inclined plane and the total flux of the entire closed surface