the electric field at a point on the axial line at a distance of 10cm from the centre of an electric dipole is 3×10³NC·¹ in air while at a diatance of 15cm,the electric field is 2×10³NC·¹ Calculate the length of an electric dipole. 3×10³NC·¹

Asked by Rinfeli567 | 7th Jul, 2020, 07:10: PM

Expert Answer:

E subscript a x i a l equals fraction numerator 1 over denominator left parenthesis 4 pi epsilon subscript 0 right parenthesis end fraction fraction numerator 2 p r over denominator left parenthesis r squared minus a squared right parenthesis squared end fraction
W h e n r equals 10 c m equals 0.1 m
E subscript a x i a l equals 3 cross times 10 cubed N C times to the power of 1
3 cross times 10 cubed equals 9 cross times 10 to the power of 9 cross times fraction numerator left parenthesis 2 p cross times 0.1 right parenthesis over denominator left square bracket 0.1 squared minus a squared right square bracket squared end fraction horizontal ellipsis. left parenthesis 1 right parenthesis
W h e n r equals 15 c m equals 0.15 m
E subscript left parenthesis a x i a l right parenthesis equals 2 cross times 10 cubed N C times to the power of 1
T h u s comma
2 cross times 10 cubed equals 9 cross times 10 to the power of 9 cross times fraction numerator left parenthesis 2 p cross times 0.15 right parenthesis over denominator left square bracket 0.15 squared minus a squared right square bracket squared end fraction horizontal ellipsis left parenthesis 2 right parenthesis
F r o m e q left parenthesis 1 right parenthesis a n d left parenthesis 2 right parenthesis comma
3 over 2 equals fraction numerator 0.1 ⁄ left square bracket 0.1 squared minus a squared right square bracket squared right parenthesis over denominator left parenthesis 0.15 ⁄ left square bracket 0.15 squared minus a squared right square bracket squared end fraction
1.5 equals fraction numerator 0.1 over denominator left square bracket 0.1 squared minus a squared right square bracket squared end fraction cross times fraction numerator left square bracket 0.15 squared minus a squared right square bracket squared over denominator 0.15 end fraction
fraction numerator left parenthesis 1.5 right parenthesis over denominator 0.66 end fraction equals fraction numerator left square bracket 0.15 squared minus a squared right square bracket squared over denominator left square bracket 0.1 squared minus a squared right square bracket squared space end fraction
2.27 equals fraction numerator left square bracket 0.15 squared minus a squared right square bracket squared over denominator left square bracket 0.1 squared minus a squared right square bracket squared space end fraction
T a k i n g space s q u a r e space r o o t space o n space b o t h space s i d e comma
plus-or-minus 1.5 equals fraction numerator left square bracket 0.15 squared minus a squared right square bracket over denominator left square bracket 0.1 squared minus a squared right square bracket end fraction
plus-or-minus 1.5 left parenthesis 0.01 right parenthesis minus 1.5 a squared equals 0.0225 minus a squared space

F o r space plus 1.5 left parenthesis 0.01 right parenthesis minus 1.5 a squared equals 0.0225 minus a squared
0.015 minus 1.5 a squared equals 0.0225 minus a squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
0.015 minus 0.0225 equals 1.5 a squared minus a squared
minus 0.0075 space equals space 0.5 space a squared space
a squared space equals space minus space minus 0.015 space space space... left parenthesis v a l u e space n o t space v a l i d space f o r space l e n g t h right parenthesis

F o r space minus 1.5 left parenthesis 0.01 right parenthesis minus 1.5 a squared equals 0.0225 minus a squared
minus 0.015 plus 1.5 a squared space equals space 0.0225 minus a squared space space space
minus 0.015 minus 0.0225 equals negative 1.5 a squared minus a squared
minus 0.0375 space equals space minus 2.5 space a squared
space a squared space equals space fraction numerator negative 0.0375 over denominator negative 2.5 end fraction equals 0.024
a space equals plus-or-minus 0.154
 
Length cannot be negative 
Thus, 
a = +0.154
Thus, length of an electric dipole is 
2a = 2 x 0.154 = 0.308 m 

Answered by Shiwani Sawant | 9th Jul, 2020, 12:05: AM

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