A long, straight wire is surrounded by a hollow metal cylinder whose axis coinci

Question

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of ?, and the cylinder has a net charge per unit length of 2?. From this information, use Gauss's law to find the following. (Use any variable or symbol stated above along with the following as necessary: e0 and p.)
(a) the charge per unit length on the inner surface of the cylinder
?inner =

(b) the charge per unit length on the outer surface of the cylinder
?outer =

(c) the electric field outside the cylinder a distance r from the axis
magnitude

Explanation / Answer

let the inner and outer radii of the cylindrical shell   are 'a' and ' b ' respecively Let Charge per unit length    of the wire   = surface charge density on the cylinder    = since the cylindre is conductor the whole charge resides on the outer surface charge on the cylindre q   = *b2 L (a) charge on the wire Q   =   *L this charge induced on the inner surface of the cylindrical shell   is -Q induced surface charge density    on the inner surface of the cylindrical shell   -'     =   - Q / a2L    =   - / a2 (b) charge per unit area   is nothing but surface charge density on the outer surface of the cylinder ''     =   + '     =        + / a2 (c) Electric field at a point p with gaussian surface of radii 'r'   is Electric flux    E(2rL )   = Qenl    / 0    here Qenl     =     *L +    b2 L Elecrtic filed E = (       +    b2 L )   /   2rL E = ( +    b2 ) /2r

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