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. (c)
Solution:
- $E_{1}=\frac{k Q}{R^{2}}$, where $k=\frac{1}{4 \pi \varepsilon_{0}}$
$$ \begin{array}{ll} \Rightarrow & \quad \mathrm{m} _ 2=\frac{k(2 Q)}{R^{2}} \\ \Rightarrow & E _ 2=\frac{2 k Q}{R^{2}} \Rightarrow E _ 3=\frac{k(4 Q) R}{(2 R)^{3}} \\ \Rightarrow \quad E _ 3=\frac{k Q}{2 R^{2}} \end{array} $$
