A particle A of charge q placed near a uniformly charged infinite plane sheet with surface charge density sigma experiences a force f1, When this particle is placed near an infinite metal plate with surface charge density sigma , it experiences a force f2 .Then what is  f1/f2 equal  to?
A) 1
B) 2
C) 1/2
D) 3
Please explain.

Asked by Kb Aulakh | 27th Apr, 2015, 11:49: PM

Expert Answer:

The electric field due to a infinite plane sheet is
 
begin mathsize 14px style straight E subscript 1 equals fraction numerator straight sigma over denominator 2 straight epsilon subscript 0 end fraction end style
 
Hence, the force experienced by a charge q placed near the sheet is
 
begin mathsize 14px style straight F subscript 1 equals qE subscript 1 equals fraction numerator qσ over denominator 2 straight epsilon subscript 0 end fraction end style
 
Now, the electric field due to a infinite metal plate is
 
begin mathsize 14px style straight E subscript 2 equals straight sigma over straight epsilon subscript 0 end style
 
Hence, the force experienced by a charge q placed near the plate is
 
begin mathsize 14px style straight F subscript 2 equals qE subscript 2 equals qσ over straight epsilon subscript 0 end style
 
Therefore, we get
 
begin mathsize 14px style straight F subscript 1 over straight F subscript 2 equals fraction numerator qσ over denominator 2 straight epsilon subscript 0 end fraction cross times straight epsilon subscript 0 over qσ equals 1 half end style

Answered by Romal Bhansali | 28th Apr, 2015, 10:55: AM

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