1
GATE EE 2007
+2
-0.6
A solid sphere made of insulating material has a radius $$R$$ and has a total charge $$Q$$ distributed uniformly in its volume. What is the magnitude of the electric field intensity, $$E,$$ at distribution $$r\left( {0 < r < R} \right)$$ inside the sphere?
A
$${1 \over {4\pi {\varepsilon _0}}}{{{Q_r}} \over {{R^3}}}$$
B
$${3 \over {4\pi {\varepsilon _0}}}{{Qr} \over {{R^3}}}$$
C
$${Q \over {4\pi {\varepsilon _0}{r^2}}}$$
D
$${1 \over {4\pi {\varepsilon _0}}}{{QR} \over {{r^3}}}$$
2
GATE EE 2003
+2
-0.6
A parallel plate capacitor has an electrode area of $$100$$ $$m{m^2}$$, with a spacing of $$0.1$$ $$mm$$ between the electrodes. The dielectric between the plates is air with a permittivity of $$8.85 \times {10^{ - 12}}\,\,F/m.$$ The charge on the capacitor is $$100$$ $$V$$. The stored energy in the capacitor is
A
$$8.85\,\,pJ$$
B
$$440\,\,pJ$$
C
$$22.1\,\,nJ$$
D
$$44.3\,\,nJ$$
3
GATE EE 2003
+2
-0.6
A point charge of $$+1$$ $$nC$$ is placed in a space with a permittivity of $$8.85 \times {10^{ - 12}}\,F/m$$ as shown in Fig. The potential difference $${V_{PQ}}$$ between two points $$P$$ and $$Q$$ at distance of $$40mm$$ and $$20$$ $$mm$$ respectively from the point charge is
A
$$0.22$$ $$kV$$
B
$$-225$$ $$V$$
C
$$-2.24$$ $$kV$$
D
$$15$$ $$V$$
4
GATE EE 2003
+2
-0.6
A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($${t_1}$$ and $${t_2}$$) as shown in Fig. The two different dielectric materials are separated by a conducting foil $$F.$$ The voltage of the conducting foil is
A
$$52$$ $$V$$
B
$$60$$ $$V$$
C
$$67$$ $$V$$
D
$$33$$ $$V$$
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