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CBSE Class 12-science Answered

Please explain in simple language.. A long charged cylinder of linear charge density +lambda 1 is surrounded by a hollow coaxial conducting cylinder of linear charge density -lambda 2. Use Gauss's law to obtain expression for the electric field at (1)a point in the space between the cylinders, (2)outside the larger cylinder.   
Asked by lekhakarthikeyan | 20 Aug, 2018, 12:00: AM
answered-by-expert Expert Answer
Gauss's law states that " total electrical flux through a closed surface equals the charge contained in the enclosed volume divided by εo "
( εo is the permitivity of the medium enclosed by the surface)
 
Mathematically, begin mathsize 12px style contour integral E times d a space equals space q over epsilon subscript o end style ................(1)
It is assumed the charged cylinders are infinitely long. 
 
To get electric field inside the charged coaxial cylinders, we consider an imaginary cylinder of radius r1 and of length l1 as shown in figure.
Due to infilint length, electric field is perpendicular to the curved surface of this imaginary cylinder and the field is uniform.  
hence eqn.(1) can be written for this imaginary cylinder as,
 
Er × 2πr1l = (λ1 × l1 ) / εo or Er = λ1 / ( 2πεor1 )  
(subscript r is used to indicate, field is in radial direction)
 
In same way electric field at a point outside the larger radius cylinder, Er = ( λ1 - λ2 )/ ( 2πεor2 )
Answered by Thiyagarajan K | 20 Aug, 2018, 04:48: PM
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