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CBSE Class 12-science Answered

derive an expression for electric field intensity at a point on the axial line of a dipole. also determine its direction.
Asked by Balan | 26 Mar, 2018, 01:05: PM
answered-by-expert Expert Answer
Figure given above illustrates the procedure to get electric field at a distance r in axial line.
E+ is the field due to positive charge +q, E- is the field due to negative charge -q
 
begin mathsize 12px style E subscript plus minus space E subscript minus space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction open square brackets 1 over open parentheses r minus d close parentheses squared space minus space 1 over open parentheses r plus d close parentheses squared close square brackets space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction 1 over r squared open square brackets open parentheses 1 minus d over r close parentheses to the power of negative 2 end exponent space minus space open parentheses 1 plus d over r close parentheses to the power of negative 2 end exponent close square brackets sin c e space d over r less than less than space 1 space space comma space w e space c a n space w r i t e E subscript plus minus space E subscript minus space equals space fraction numerator q over denominator 4 pi epsilon subscript 0 end fraction 1 over r squared open square brackets 1 plus fraction numerator 2 d over denominator r end fraction minus 1 plus fraction numerator 2 d over denominator r end fraction close square brackets space equals space fraction numerator 4 q d over denominator 4 pi epsilon subscript 0 end fraction 1 over r cubed i f space w e space d e f i n e space d i p o l e space m o m e n t space p space equals space q cross times 2 d space comma space t h e n E subscript plus minus space E subscript minus space equals fraction numerator 2 p over denominator 4 pi epsilon subscript 0 end fraction 1 over r cubed end style
magnitude of E+ is grater than magnitude of E- , hence the direction of net field is along the direction of E+
Answered by Thiyagarajan K | 26 Mar, 2018, 10:49: PM

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