(3)Alinechargeanda chargedconductingcylinderPAn image line charge - p, is put in to represent the charge onthe cylinder and placed parallelto it,at a distanced from the axisThe electric field intensity produced by an infiniteline charge ofdensitypigiven byE :2元rThe electric potential with respectto a referencepoint ro at adistancer from the line electric charge is0=-1,Edr-Plin2元8U
l （3）A line charge and a charged conducting cylinder. P a f d r -l O An image line charge is put in to represent the charge on the cylinder and placed parallelto it, at a distance d from the axis. − l r l r E e 2π = The electric potential with respect to a reference point at a distance r from the line electric charge is 0 r = − = r r E r l r r 0 ln 2π d 0 The electric field intensity produced by an infinite line charge of density given by l
If ro is also taken as the reference point for the electric potentialproduced by the image line charge- p,, then p,and - p, produce anelectric potential at a point P on the surface of the cylinder given byPI0902元82元8Since the conducting cylinderis an equipotential body,in orderto satisfy this boundary condition the ratio must be a constant.wefindLeadfU7
If is also taken as the reference point for the electric potential produced by the image line charge , then and produce an electric potential at a point P on the surface of the cylinder given by − l 0 r l − l − = r r r r l l P 0 0 ln 2π ln 2π = r r l ln 2π Since the conducting cylinder is an equipotential body, in order to satisfy this boundary condition the ratio must be a constant. r r f a d 2 = a d f a r r = = Let , we find