Complete Question
The complete question is shown on the first uploaded image
Answer:
The wavelength is
Explanation:
From the question we are told that
The distance of the slit to the screen is
The order of the fringe is m = 6
The distance between the slit is
The fringe distance is
Generally the for a dark fringe the fringe distance is mathematically represented as
=>
substituting values
=>
=>
a) q_shell = -Q , b) q_shell = -Q
a) We can solve this exercise using Gauss's law
Ф = ∫ E. dA = /ε₀
For this we use a Gaussian surface that takes advantage of the symmetry of the problem, we select a sphere where this force of the spherical plastic shell.
In this case, the electric field lines coincide with the radii of the sphere and the scalar product reduces to the algebraic product, the area of the sphere
A = 4 π r²
fi = E 4π r² = q_{int} /ε₀
apply this formula to our case, we have that the charge inside the Gaussian sphere is
q_{int} = q_sphere + q_shell
the charge of the sphere is Q and the requirement is that there is no electric field outside the Gaussian sphere, for this, the net charge inside it must be zero
0 = Q + q_shell
q_shell = -Q
b) In Gauss's law, only the charge inside the Gaussian surface matters, not its position, therefore if the charge is not in the center the result remains the same.
q_shell = -Q
Please check the attached attachment for the detailed answer.
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