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In: Physics

A cube with side a is located at the origin,a point charge q is placed at...

A cube with side a is located at the origin,a point charge q is placed at each vertex .find the charge density in term of Dirac delta function

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Expert Solution

It is given that the cube is located at the origin.

A cube has 8 vertexes.

Suppose that one of the vertexes are at the origin.

Since there is a point charge q at each vertex of the cube, the locations of charges are

  • (0,0,0)
  • (0,0,a)
  • (0,a,0)
  • (a,0,0)
  • (0,a,a)
  • (a,0,a)
  • (a,a,0)
  • (a,a,a)

We have to find the charge distribution such that the value of charge is q at these points and zero elsewhere.

This can be easily done with dirac delta function. Suppose that the value of a function ts equal to A at (a,b,c) and zero elsewhere.

This point can be expressed as a dirac delta function as

The integral is done from - infinity to + infinity.

Thus the charge configuration as mentioned above is represented as

genius_generous answered 2 years ago
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