Question

A charge of uniform linear density 2.00 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.60 cm, outer radius = 9.80 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 15.4 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?

Answer 1

Answer:

(a) E=233.56 N/C

(b) The surface charge density of inner surface  σ= -5.69×10⁻⁹C/m²

(c)The surface charge density of outer surface  σ= 3.25×10⁻⁹C/m²

Explanation:

For Part (a)

The magnitude of the electric field at distance of 15.4 cm from the axis of the shell is given by:

E=λ/2πε₀r

Substitute the given values

$E=\frac{2.00*10^{-9} }{2\pi 8.854*10^{-12}*0.154 }\\ E=233.56N/C$

Since the nonconducting rod positively charged,it induces a negative charge -q on the inner surface of conducting shell and a positive charge +q on the outer surface of conducting shell,so the net charge of conducting shell is zero

Part (b)

The surface charge density of inner surface is given by:

σ=-q/A

$=\frac{-q}{2\pi r_{inner} l}\\ =\frac{\frac{-q}{l} }{2\pi r_{inner}}$

= -λ/2πr

$=\frac{-2.0*10^{-9} }{2\pi (0.056)}\\ =-5.69*10^{-9}C/m^{2}$

Part(c)

Similarly the surface charge density on the outer surface of the cylindrical shell given by:

σ=λ/2πr

$=\frac{2.0*10^{-9} }{2\pi 0.098}\\ =3.25*10^{-9}C/m^{2}$