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Coulomb's Law - Mathematical Form

Two uniformly...

Question

Two uniformly charged spheres with radii $r_{1}$ & $r_{2}$ and charges $Q_{1}$ & $Q_{2}$ are separated by distance d (from the periphery of the two spheres). What is the magnitude of force on $Q_{2}$ due to $Q_{1}$ ?

$F = \frac{K Q_{1} Q_{2}}{d^{2}}$

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$F = \frac{K Q_{1} Q_{2}}{(d + r_{2})^{2}}$

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$F = \frac{K Q_{1} Q_{2}}{(d + r_{1}})^{2}$

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$F = \frac{K Q_{1} Q_{2}}{(d + r_{1} + r_{2})^{2}}$

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Solution

The correct option is D
$F = \frac{K Q_{1} Q_{2}}{(d + r_{1} + r_{2})^{2}}$

Coulomb’s law is applicable only to point charges. But for symmetric shaped uniformly charged objects like spheres, we can consider the whole charge to be located at the centre, or else we need integration.

Since separation between centres of two spheres is $d + r_{1} + r_{2}$ ,

Applying Coulomb’s Law,

$| F | = \frac{K Q_{1} Q_{2}}{(d + r_{1} + r_{2})^{2}}$

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Two uniformly charged spheres with radii r1 & r2 and charges Q1 & Q2 are separated by distance d (from the periphery of the two spheres). What is the magnitude of force on Q2 due to Q1?

Two uniformly charged spheres with radii $r_{1}$ & $r_{2}$ and charges $Q_{1}$ & $Q_{2}$ are separated by distance d (from the periphery of the two spheres). What is the magnitude of force on $Q_{2}$ due to $Q_{1}$ ?