If the total charge inside a closed surface is known but the distribution (shape

Question

If the total charge inside a closed surface is known but the distribution (shape) of the charge is unknown, can Gauss's Law be used to find the electric field? Explain. Two infinite planes of charge are parallel to each other, a distance d apart. The left one has charge density equal to +sigma, while the right one has charge density -sigma. In class we discovered that the field of just a single sheet of +sigma produces a uniform field pointing away from it equal to E = sigma/2 epsilon_0. Find the magnitude and direction of the field to the left of the positive plate to the right of the negative plate between the two plates

Explanation / Answer

gauss law can be apply when charge is distributed uniformly and symmetric

To the left of positive plate net electric field wil be zero because magnitude of electric field due to positive plate= magnitude of electric field due to negative plate but opposite in direction

To the right of negative plate net electric field is zero reason same as above

Between plate net electric field wil be E = /permittivity of free space

electric field due to positive plate +electric field due to negative plate =net electric field (because both wil act in the same direction )i.e.towards negative plate

So direction of net electric field wil be towards negative plate

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