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At the  four corners of a square  of side 1 m , +Q, -Q, +Q,-Q charges are fitted. Find intensity at the center of square. pls ps explain in detail and in lucid language

Asked by ppratim02 22nd June 2016, 6:18 PM
Answered by Expert
Answer:
Let the side of the square be 'a' = 1 m
 
 
begin mathsize 12px style Diagonal space of space the space square space is space straight a square root of 2. space space
The space distance space from space any space charge space to space the space centre space of space the space square space is space half space this comma space straight i. straight e. space fraction numerator straight a square root of 2 over denominator 2 end fraction space space space
The space field space at space the space centre space from space any space charge space is space fraction numerator 1 over denominator 4 πε subscript straight o end fraction straight q over open parentheses fraction numerator straight a square root of 2 over denominator 2 end fraction close parentheses squared space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 4 straight q over denominator 2 straight a squared end fraction equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction
The space apostrophe vertical apostrophe space components space cancel space and space each space each space horizontal space component space is space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction cross times space cos left parenthesis 45 right parenthesis equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction space
rightwards arrow equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator straight a squared end fraction
The space total space is space due space to space all space the space four space charges
space rightwards arrow straight E equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator straight a squared end fraction cross times 4
But space straight a space equals 1
space rightwards arrow straight E equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator 1 end fraction cross times 4
space rightwards arrow straight E equals space fraction numerator square root of 2 straight q over denominator πε subscript straight o end fraction end stylebegin mathsize 12px style Diagonal space of space the space square space is space straight a square root of 2. space space
The space distance space from space any space charge space to space the space centre space of space the space square space is space half space this comma space straight i. straight e. space fraction numerator straight a square root of 2 over denominator 2 end fraction space space space
The space field space at space the space centre space from space any space charge space is space fraction numerator 1 over denominator 4 πε subscript straight o end fraction straight q over open parentheses fraction numerator straight a square root of 2 over denominator 2 end fraction close parentheses squared space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 4 straight q over denominator 2 straight a squared end fraction equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction
The space apostrophe vertical apostrophe space components space cancel space and space each space each space horizontal space component space is space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction cross times space cos left parenthesis 45 right parenthesis equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator 2 straight q over denominator straight a squared end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction space
rightwards arrow equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator straight a squared end fraction
The space total space is space due space to space all space the space four space charges
space rightwards arrow straight E equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator straight a squared end fraction cross times 4
But space straight a space equals 1
space rightwards arrow straight E equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction cross times fraction numerator square root of 2 straight q over denominator 1 end fraction cross times 4
space rightwards arrow straight E equals space fraction numerator square root of 2 straight q over denominator πε subscript straight o end fraction end style
Answered by Expert 24th June 2016, 12:17 PM
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