Question

What is the total flux through the face of the cube with side of the length A if a charge Q is placed at: 1) A: a corner of the cube 2) B: mid point of the edge of the cube 3) C: center of the face of the cube 4) D: mid point of B and C

Answer 1

$$\begin{gathered} 1)WhenchargeQisplacedatonecornerofthecube,byapplyingGauss\text{'}slawofflux,thereisnofluxpas\sin gthroughtheface. \\ 2)EvenifthechargeQisplacedatthemidpointBoftheedge,thereisnofluxpas\sin gthroughthefacebecausenochargeisenclosedbythecube. \\ 3)WhenchargeQisplacedatthecentreCofthecubethenfluxpas\sin gthroughtheonefaceofthecube=\left(\frac{\phi }{6}\right)=E\times A^2.HerelengthofthesideofcubeisA. \\ 4)WHENTHECHARGEISPLACEDatthemidpointofBandC,inthiscasethechargecomesinsidethecube,thereforefluxpas\sin gthroughoneface \\ =\left(\frac{\varphi }{6}\right)=E\times A^2. \end{gathered}$$