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CBSE Class 11-science Answered

Four identical charges are fixed at corners of a square of side a. Find field at point p which is at a distance z lying on the line perpendicular to the plane of square passing through centre of square
Asked by arushidabhade | 26 Apr, 2020, 11:39: PM
answered-by-expert Expert Answer
 
Let ABCD is a square of side a and charges of equal magnitude and sign are placed at four corners as shown in figure.
 
P is a point at a distance z from centre O of square .
 
Electric field at P due to each charge is in a direction that makes angle θ with the vertical line
joining O and P as shown in figure.
 
If we resolve this electric field in to two comonenets, i.e., one vertical component along the line OP and
other horizontal component
 
perpendicular to line OP, then horizontal component will be cancelled due to placement of charges at
opposite corners along the diagonal of square ABCD.
 
Hence resulatant electric field E at P due to point charges placed at corner of square ABCD is given by
 
begin mathsize 14px style E space equals space 4 space cross times fraction numerator q over denominator 4 pi epsilon subscript o open parentheses z squared plus space begin display style a squared over 2 end style close parentheses end fraction cross times space cos theta space equals space fraction numerator 4 cross times q over denominator 4 pi epsilon subscript o open parentheses z squared plus space begin display style a squared over 2 end style close parentheses end fraction cross times fraction numerator z over denominator square root of z squared plus space a squared over 2 end root end fraction end style
 
begin mathsize 14px style E space equals space space fraction numerator 4 cross times q cross times z over denominator 4 pi epsilon subscript o open parentheses z squared plus space begin display style a squared over 2 end style close parentheses to the power of begin display style bevelled 3 over 2 end style end exponent end fraction end style
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