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CBSE Class 12-science Answered

explain coulambs law give unit and dimensions of electrostatics constant and coulambs law in vector form with superposition principle
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Asked by bhatig9772 | 09 Jan, 2023, 06:48: PM
answered-by-expert Expert Answer
Coulomb's law
 
Electrostatic force begin mathsize 14px style F with rightwards arrow on top end style between two charges q1 and q2 that are separated by a distance d is
begin mathsize 14px style F with rightwards arrow on top space equals space K space fraction numerator q subscript 1 space q subscript 2 over denominator d squared end fraction space r with hat on top end style
where K = 1/(4begin mathsize 14px style πε subscript straight o end style) is Coulomb's constant or electrostatic constant and begin mathsize 14px style r with hat on top end style is unit vector
along the direction of line joining charges q1 and q2 .
 
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Units of electrosatatic constant K = 1/(4begin mathsize 14px style πε subscript straight o end style) is  N m2 C-2
 
Dimension of Newton N = M L T-2
 
Coulomb is current × time . Hence dimension of coulomb = A T-1
 
Hence dimension of electrostatic constant =  M L T-2  ×  L2  × A T-2 = M L3 T-3
 
( M is mass , L is length and A is Ampere  )
 
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Coulomb's law in vector form and superposition principle
 
Let q be the test charge at position vector begin mathsize 14px style r with rightwards arrow on top end style as shown in figure.
Charge q1 is at position vector begin mathsize 14px style stack r subscript 1 with rightwards arrow on top end style .  charge q2 is at position vector begin mathsize 14px style stack r subscript 2 with rightwards arrow on top end style .. So on ....
Net force begin mathsize 14px style F with rightwards arrow on top end styleexperienced by charge q is
begin mathsize 14px style F with rightwards arrow on top space equals K space sum for i of space space space fraction numerator q space q subscript i over denominator d subscript i end fraction space space stack r subscript i with hat on top end style
where di = begin mathsize 14px style open vertical bar stack r subscript i with rightwards arrow on top space minus space r with rightwards arrow on top close vertical bar end style  and   begin mathsize 14px style stack r subscript i with hat on top space equals space fraction numerator stack r subscript i space with rightwards arrow on top space minus space r with rightwards arrow on top over denominator open vertical bar stack r subscript i space with rightwards arrow on top space minus space r with rightwards arrow on top close vertical bar end fraction end style
 

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