Question

An infinitely long uniform line charge distribution of
charge per unit length ???? lies parallel to the y-axis in the
y-z plane at z =√3/2a(see figure). If the magnitude of
the flux of the electric field through the rectangular
surface ABCD lying in the x-y plane with its center at
the origin is ????L/n????₀ (????₀= permittivity of free space), then
the value of n is

Answer 1

Explanation:

Given An infinitely long uniform line charge distribution of charge per unit length λ lies parallel to the y-axis in the y-z plane at z =√3/2a (see figure). If the magnitude of  the flux of the electric field through the rectangular  surface ABCD lying in the x-y plane with its center at  the origin is λL/nε₀ (ε₀= permittivity of free space), then  the value of n is

• Now the line is parallel in the y-z plane at z = √3/2 a. we need to find the value of n.
• Now let there be a point and consider it as a line and the linear density of it is positive. Now the symmetry will be either circular or cylindrical. So a plate is kept and the length of the plate is a. In the cylindrical symmetry there are flux on all four sides.So the amount of flux passing through ABCD is to be found.
• So flux through cylinder φ = q enclose / εo
•               But q = λ L
•                 Or λ = q/L
•                                   So φ = λ L / εo
•           Now an infinitely long rod is placed and its length is given as √3 /2 a. the line bisects the mid point and it will be a/2
•           Therefore tan theta = a/2 / √3 / 2 a
•                                                = 1/√3
•                                  So theta = 30 degree
• Now 360 degree can be divided as 6 times of 60 degree
•         So flux φ = λ L / 6 εo will be the flux passing through ABCD.
• Therefore the value of n will be n = 6

Reference link will be

https://brainly.in/question/8720714