CBSE Class 12-science Answered

Please solve this question

Asked by shinghip6 | 17 Jul, 2022, 16:36: PM

Expert Answer

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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 E_R 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 / ( 4πε_o ) 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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