A very long straight thread is oriented at right angles to an infinite conducting plane; its end is separated from the plane by a distance λ . The thread carries a uniform charge of linear density λ. Suppose the point O is the trace of the thread on the plane. Find the surface density of the induced charge on the plane
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
σ = 
;
σ(r) = 
Sol.
Using image method:
Calculation of field at point O due to charge of image.
E = 
Since charge density at O is σ then.
⇒ 
Field at point P is only along y-axis because field in the x-direction will be cancelled
Hence field due to plane = field due to (–λ) image charge in y direction
E y = 
= 
E y = 
= 
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