A charge of uniform linear density 2.40 nC/m is distributed along a long, thin,

Question

A charge of uniform linear density 2.40 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.80 cm, outer radius = 10.6 cm). The net charge on the shell is zero. (a) What is the magnitude (in N/C) 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?

A charge of uniform linear density 2.40 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.80 cm, outer radius = 10.6 cm). The net charge on the shell is zero. (a) What is the magnitude (in N/C) 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?

Explanation / Answer

(a) Acccording to gauss law   The elecctric flux = E ( 2rl )    = q / _0 Here   q    = linear charge density *   length of the rod =   2.4*10^-9 C / m * l E     =   *l / 2rl _0    =   * / 2r _0   Here r =  0.154 m , _0   =   8.85*10^-12 C^2 / N.m^2 plug all values we get E = 0.283*10^3 N/C (b) surface charge density on the inner surface of the shell _in    = - q /2rl   =      -   *l   / 2rl   = - / 2r Here r   inner radius = 0.048m _in    =   -   7.96*10^-9 C (c) surface charge density on the outer surface of the shell   _out    =  q /2rl   =        *l   / 2rl   = / 2r   Here r = outer radius = 0.106 m _out   = +3.60*10^-9 C

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