A cylindrical shell of radius 7.00 cm and length 260 cm has its charge uniformly distributed on itscurved surface. The magnitude of the electric field at a point20.0 cm radially outward from its axis(measured from the midpoint of the shell) is 36.0 kN/C.(a) Use approximate relationships to find thenet charge on the shell.(b) Use approximate relationships to find theelectric field at a point 4.00 cm from theaxis,measured radiallyoutward from the midpoint of the shell.

b) Since no charge is enclosed by the imaginary surface at the given radial distance so the electric field measured outward form the axis is also zero.

Explanation:

Given:

radius of the cylindrical shell, [tex]r=0.07\ m[/tex]

length of the cylindrical shell, [tex]h=2.6\ m[/tex]

magnitude of electric field at 20 cm from the axis, [tex]E=36000\ N.C^{-1}[/tex]

a)

[tex]\oint E.dA=\frac{Q_{enc}}{\epsilon_0}[/tex]

[tex]\Rightarrow \vert E\vert \times 2\pi.r'.h=\frac{Q_{enc}}{\epsilon_0}[/tex]

[tex]36000\times 2\pi\times 0.2\times 2.6\times 9\times 10^{-9}=Q_{enc}[/tex]

[tex]Q_{enc}=1.06\times 10^{-3}\ C[/tex]

b)

Given radial distance, [tex]r=0.04\ m[/tex]

[tex]\oint E.dA=\frac{Q_{enc}}{\epsilon_0}[/tex]

[tex]\Rightarrow \vert E\vert \times 2\pi.r'.h=\frac{Q_{enc}}{\epsilon_0}[/tex]

[tex]\frac{Q_{enc}}{\epsilon_0} =\vert E\vert\times 2\pi.r'.h[/tex]

[tex]\frac{Q_{enc}}{\esilon_0} =0[/tex]

Since no charge is enclosed by the imaginary surface at the given radial distance so the electric field measured outward form the axis is also zero.