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Charging by Friction

Charges Q, 2Q...

Question

Charges $Q, 2 Q$ and $4 Q$ are uniformly distributed in three dielectric solid spheres $1, 2$ and $3$ of radii
$R / 2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of sphere $1, 2$ and $3$ are $E_{1,} E_{2}$ and $E_{3}$ respectively, then

A

E_{3} > E_{1} > E_{2}

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B

E_{2} > E_{1} > E_{3}

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C

E_{3} > E_{2} > E_{1}

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D

E_{1} > E_{2} > E_{3}

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Solution

The correct option is B $E_{2} > E_{1} > E_{3}$

$E_{1} = \frac{K Q}{R^{2}}$
$E_{2} = \frac{K (2 Q)}{R^{2}} = \frac{2 K Q}{R^{2}}$
$E_{3} = \frac{K (4 Q) R}{8 R^{3}} = \frac{K Q}{2 R^{3}}$
$E_{2} > E_{1} > E_{3}$

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