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A cube of side b has a charge q at each ...

A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the center of the cube.

A

`(4q)/(3piepsi_(0)x)`

B

`(4q)/(sqrt3pi epsi_(0)x)`

C

`(3q)/(4 pi epsi_(0)x)`

D

`(2q)/(sqrt3piepsi_(0)x)`

Text Solution

Verified by Experts

The correct Answer is:
B
The length of diagonal of the cube of each side x is `sqrt(3x^2)=xsqrt3`
`therefore` Distance between centre of cube and each vertex, `r=(xsqrt3)/2`
Now , potential, V=`1/(4piepsilon_0)q/r`
Since cube has 8 vertices and 8 charges each of value q are present there `therefore V=1/(4piepsilon_o)"8q"/((xsqrt3)/2)="4q"/(sqrt3piepsilon_o x)`
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