Two coaxial cylindrical conductors are shown in perspective and cross-section above. The inner cylinder has radius a = 2 cm, length L = 10 m and carries a total charge of Qinner = + 8 nC (1 nC = 10-9 C). The outer cylinder has an inner radius b = 6 cm, outer radius c = 7 cm, length L = 10 m and carries a total charge of Qouter = - 16 nC (1 nC = 10-9 C). What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r = 4 cm from the origin and makes an angle of 30 degrees with the x-axis?
Ex =?

The total electric flux out of a closed surface is equal to the charge contained divided by the permittivity, according to Gauss Law.

The electric flux in a given area is calculated by multiplying the electric field by the area of the surface projected in a plane perpendicular to the field.

The given data in the problem is;

a is the inner cylinder has radius = 2 cm,

L is the length of cylinder = 10 m

[tex]\rm Q_{inner}[/tex] = + 8 nC (1 nC = 10⁻⁹ C).

b is the inner radius of outer cylinder = 6 cm

c is the outer radius of the outer cylinder = 7 cm

[tex]\rm Q_{outer}[/tex] = - 16 nC (1 nC = 10-9 C).

Eₓ is the x-component of the electric field at point P=?

Θ is the angle in degrees with the x-axis =30°

The electric field is found by the gauss law for an infinite cylinder;

[tex]\rm E=\frac{1}{2\pi} \times \frac{\lambda}{r} \\\\ \rm E=\frac{1}{2\times 3.14} \times \frac{\frac{Q}{l} }{r}\\\\ E=Ecos30^0 \\\\ E= \frac{2\times9\times10^9 \times 8 \times10^{-9}}{0.04\times0.866} \\\\ \rm E=312 N/C[/tex]

Hence the value of the electric field for the given condition is 312N/C.

To learn more about the gauss law refer to the link;

https://brainly.com/question/2854215