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CBSE Class 12-science Answered

Please solve this question
Asked by shinghip6 | 17 Jul, 2022, 04:36: PM
Expert Answer
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If there are more than one question, either first question or question specified by user is answered.
 
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Electric dipole consists of two charges of equal magnitude but opposite sign that are separated by a small distance
 
Electric dipole moment begin mathsize 14px style p with rightwards arrow on top end style is the product of charge q and distance d .
Electric dipole moment begin mathsize 14px style p with rightwards arrow on top end style  is vector quantity thta has direction from negative charge to positive charge
begin mathsize 14px style p with rightwards arrow on top end style = q begin mathsize 14px style d with rightwards arrow on top end style
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Let us consider a point P on the axis passing through mid point of dipole. Let the point P be at a distance z from centre .
 
At the point P , two charges are at equal distance from P .
 
Since the charges are equal in magnitude and opposite in direction, potential at P is zero.
 
Electric field at P due to positive charge is E+ as shown in figure .
 
Similarly electric field at P due to negative charge is E- as shown in figure .
 
Magnitude E of E+ and E- are same because magnitude of charge and distances are equal for both fields. 
 
Resultant field ER is given as
begin mathsize 14px style E subscript R space equals space 2 space cross times space K space cross times fraction numerator q over denominator open parentheses z squared plus d squared over 4 close parentheses end fraction cross times cos theta end style
where K = 1 / ( 4πεo ) is the coulomb's constant

where cosθ is given as
begin mathsize 14px style cos theta space equals space fraction numerator d divided by 2 over denominator square root of z squared plus begin display style d squared over 4 end style end root end fraction end style

Hence resultant electric field is written as
begin mathsize 14px style E subscript R space equals space space K space cross times fraction numerator q space d over denominator open parentheses z squared plus d squared over 4 close parentheses to the power of 3 divided by 2 end exponent end fraction end style
 
If we use the definition of dipole moment " p = q d  " and consider d << z , then resultant field will become
 
begin mathsize 14px style E subscript R space equals space space K space cross times p over z cubed end style
Answered by Thiyagarajan K | 18 Jul, 2022, 09:32: AM
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