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Physics-

General

Easy

Question

Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference $V subscript A end subscript minus V subscript B end subscript equals V subscript B end subscript minus V subscript C end subscript$ . If $t subscript 1 end subscript$ and $t subscript 2 end subscript$ be the distance between them. Then

$t_{1} = t_{2}$
$t_{1} > t_{2}$
$t_{1} < t_{2}$
$t_{1} \leq t_{2}$

The correct answer is: $t subscript 1 end subscript less than t subscript 2 end subscript$

Potential difference between two equipotential surfaces A and B.
$V subscript A end subscript minus V subscript B end subscript equals k q open parentheses fraction numerator 1 over denominator r subscript A end subscript end fraction minus fraction numerator 1 over denominator r subscript B end subscript end fraction close parentheses$
$equals k q open parentheses fraction numerator r subscript B end subscript minus r subscript A end subscript over denominator r subscript A end subscript r subscript B end subscript end fraction close parentheses$
$equals fraction numerator k q t subscript 1 end subscript over denominator r subscript A end subscript r subscript B end subscript end fraction$
Or
$t subscript 1 end subscript equals fraction numerator open parentheses V subscript A end subscript minus V subscript B end subscript close parentheses r subscript A end subscript r subscript B end subscript over denominator k q end fraction$
Or $t subscript 1 end subscript proportional to r subscript A end subscript r subscript B end subscript$
Similarly, $t subscript 2 end subscript proportional to r subscript B end subscript r subscript C end subscript$
Since,
$r subscript A end subscript less than r subscript B end subscript less than r subscript C end subscript comma$ therefore $r subscript A end subscript r subscript B end subscript less than r subscript B end subscript r subscript C end subscript$
$therefore blank t subscript 1 end subscript less than t subscript 2 end subscript$

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