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CBSE Class 12-science Answered

Please solve this question
Asked by shinghip6 | 17 Jul, 2022, 04:36: PM
Expert Answer
Seven questions should not be asked in single posting. Only one question per posting is allowed.
 
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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CBSE 12-science - Physics
Please solve this question
Asked by shinghip6 | 17 Jul, 2022, 04:36: PM
ANSWERED BY EXPERT
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