Question

P3 Q6 A rod of length L has a uniform positive charge per unit length 1 and total charge Q. Set up an integration to calculate the electric potential at the points:- a (a)P1 (b) P2 (c)P3 7

Answer 1

1 dret B ta a) At P P. lan set take small element at a distance from Point Pro dq= ddr = a dne L The Potential at P due to this charge element, dv= kde ka due N kodin by integrat Total Potential due to rod is ing this du as Lta v= f du ка ( olx. L a tta x a (6) At Pg. d. d² +22 dne

The charge علم = a da L 2 Potential at Pg due to this de charge element KQ du k dq da 52+d² L (x²+d2 Potential due to rodat bis rodatkis gwen by Integrate to NELo v= Saw ка dn L 5x²to2 2=0 t

(c) Pa ď Divide the rod inta infinitesimal charge elemente of length drea doe 1/ zn 4/2 AP The = The L (86)²+d2 charge of charge element, da a dre dq = a dne potential at Pz due to charge element is di = K da AP3 dv= KO dae V² +d² find the potential for the whole rod, integrata L To this potential

tar ar L V Ve sdu Ке dne Sx²+ da -Lg This is the Integration which gives at P3. potential