Electrostatics 1 Question 6
6. 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 spheres 1,2 and 3 are $E _1, E _2$ and $E _3$ respectively, then
(2014 Adv.)
Sphere-1
Sphere-2
(a) $E _1>E _2>E _3$
(b) $E _3>E _1>E _2$
(c) $E _2>E _1>E _3$
(d) $E _3>E _2>E _1$
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Answer:
Correct Answer: 6. (d)
Solution:
- $E _1=\frac{k Q}{R^{2}}$, where $k=\frac{1}{4 \pi \varepsilon _0}$
$$ \begin{array}{ll} \Rightarrow & \quad m _2=\frac{k(2 Q)}{R^{2}} \\ \Rightarrow & E _2=\frac{2 k Q}{R^{2}} \Rightarrow E _3=\frac{k(4 Q) R}{(2 R)^{3}} \\ \Rightarrow \quad E _3=\frac{k Q}{2 R^{2}} \end{array} $$
