Line Charge and Charged Cylindrical Shell

[hime]

Homework Statement

An infinite line of charge with linear density λ = 8.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.9 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -659 μC/m3.

What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.45 cm along a line that makes an angle of 30 deg with the x-axis?

What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.45 cm along a line that makes an angle of 30 deg with the x-axis?

Homework Equations

E.dA = q/ eo
Area of the cylinder = 2*pi* r* length

The Attempt at a Solution

Using the above formula, I got:
Ex(R) =10914190.5*cos(30) but its wrong.

The y-component of the electric field at point R is not zero. The charges do produce a non-zero field at point R. You can determine the direction of the field at point R from the symmetry of the charge distribution.

 

[mark726]

To find the x-component of the electric field at point R, we can use the formula E = kλ/r, where k is the Coulomb constant, λ is the linear charge density, and r is the distance from the line of charge. In this case, r = 1.45 cm. Plugging in the values, we get:

Ex(R) = (9*10^9)(8.8*10^-6)/(1.45*10^-2) = 6.06 N/C

To find the y-component of the electric field at point R, we can use the formula E = kρr/3, where k is the Coulomb constant, ρ is the volume charge density, and r is the distance from the center of the insulating shell. In this case, r = 1.45 cm. Plugging in the values, we get:

Ey(R) = (9*10^9)(-659*10^-6)(1.45*10^-2)/3 = -3.02 N/C

Therefore, the values for Ex(R) and Ey(R) are 6.06 N/C and -3.02 N/C, respectively.