An anxious physicist worries that the two metal shelves of a wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area 1.00×102m2 and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored. (d) The actual shelves have an area 100 times smaller than these hypothetical shelves. Are his fears justified?

λ  = 4.023 10⁻⁷ m

Explanation:

The double-slit interference phenomenon is described by

          d sin θ = (m + ½) λ          destructive interference

          d sin θ = m λ                  constructive interference

we can use trigonometry

         tan θ = y / L

how these experiments occur for small angles

         tan θ = sin θ/cos θ = sin θ

         sin θ = y / L

we substitute

        d y / L = (m + ½) λ        destructive interference

        d y / L = m λ                 constructive interference

with the expression for constructive interference we look for the separation of the slits

        d = m λ L / y

        d = 1 603 10⁻⁹ 3 /4.84 10⁻³

        d = 3.738 10⁻⁴ m

Now let's analyze the case where the distance for constructive and destructive interference occurs at the same point y = 4.84 mm = 4.84 10⁻³m

          d y / L = (m + ½)  λ

          λ =

the first strip is for m = 1  

let's calculate

         λ  =

         λ  = 4.023 10⁻⁷ m