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CBSE Class 12-science Answered

An infinitely large thin plane sheet has an uniform surface charge density +σ . Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point distance r in front of the charged plane sheet.   
Asked by ritikabehera01 | 04 Mar, 2019, 12:19: AM
answered-by-expert Expert Answer
This question is wrongly formulated.
 
Infinite charged plate is an imaginary object in electrostatics.
 
Electric field near to infinite charged plate  = σ/(2εo)  , where σ is surface charge density and εo is permitivity of free space.
 
But far away from infinite charged plate above expression for electric field is not valid.
 
For example if charged plate's dimensions are in metre, the above expression for electric field is valid for few cm , may be around 10 cm,
but not around a metre away.
 
Hence it is not possible to calculate the workdone to bring a point charge from infinity to a point near to plate, because very far away
electric field is not expressed by mathematical expression unless exact plate dimension are given.
 
Let us do this problem in another way. Let us calculate the workdone for moving a point charge q from a point P at a distance R from plate,
where the elecric field σ/(2εo) is valid, to the point Q which is very near to plate at a distance r from plate.
 
Workdone = begin mathsize 16px style negative integral subscript R superscript r space q space E space d r space space equals space minus integral subscript R superscript r q space fraction numerator sigma over denominator 2 epsilon subscript 0 end fraction space d r space equals space fraction numerator q space sigma over denominator 2 epsilon subscript 0 end fraction left square bracket space R space minus space r space right square bracket space space space J o u l e s end style
in the above expression -ve sign is considered, because we assume distances are measured from plate,
where as charge is moved in opposite direction
Answered by Thiyagarajan K | 04 Mar, 2019, 09:03: AM

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