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CBSE Class 12-science Answered

Semi infinite rod having linear charge density  lemda . Find the electric field at a distance  r from the one end of rod & normal  to the rod .
Asked by Shravanraj280 | 25 Nov, 2019, 12:22: AM
answered-by-expert Expert Answer
 
Figure shows a semi infinite line having linear charge λ per unit length.
 
Electric field dE at P for a small line element dl that is having charge λdl and is at a distance l from left end O,  is given by

 

............................................(1)
Electric field given in eqn.(1) is in the direction AP that can be resolved into two components,
i.e., dEx and dEy as shown in figure
 
..............................(2)
 
...............................(3)
 
Electric field Ex due to whole line element is obtained by integrating eqn.(2)
 
.....................(4)
 
Above integration is solved using substitution , l = d tanθ .  we get Ex = [ λ / (4πεo) ] (1/d)
 
Similarly by integrating eqn.(3), we get, Ey = [ λ / (4πεo) ] (1/d)
 
Hence net electric field E = [ Ex2 + Ey2 ]1/2 = [ λ / (4πεo) ] (√2/d)
Answered by Thiyagarajan K | 25 Nov, 2019, 08:57: AM
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