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 1 year ago

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