a point charge q is placed at the corner of a cube with side l find flux through entire surface and flux through each face
a point charge q is placed at the corner of a cube with side l find flux through entire surface and flux through each face
The total flux from a charge q is q/ε₀ (Gauss's law). If the charge is on the corner of a cube, some of the flux enters the cube and leaves through some of its faces. But some of the flux doesn't enter the cube.
Suppose the charge is at the very centre of this hypothetical cube - it is on a corner of each of the 8 cubes. An equal amount of flux will spread outwards through each of the cubes (symmetry)
Since the flux is shared between 8 cubes, the flux through each is (1/8)q/ε₀ [entire surface]
Now flux(1/8th) will pass through three of the faces of (smaller)cube and three faces wont have any effect(the ones from which the cube passes)
This 1/8th will be divided into 3 parts again.
so the total will be (1/24)q/ε₀ from each face
The total flux from a charge q is q/ε₀ (Gauss's law). If the charge is on the corner of a cube, some of the flux enters the cube and leaves through some of its faces. But some of the flux doesn't enter the cube.
Suppose the charge is at the very centre of this hypothetical cube - it is on a corner of each of the 8 cubes. An equal amount of flux will spread outwards through each of the cubes (symmetry)
Since the flux is shared between 8 cubes, the flux through each is (1/8)q/ε₀ [entire surface]
Now flux(1/8th) will pass through three of the faces of (smaller)cube and three faces wont have any effect(the ones from which the cube passes)
This 1/8th will be divided into 3 parts again.
so the total will be (1/24)q/ε₀ from each face
