1
GATE EE 2011
+2
-0.6
A capacitor is made with a polymeric dielectric having an $$\varepsilon_0$$ of 2.26 and a dielectric breakdown strength of 50 kV/cm. The permittivity of free space is 8.85 pF/m. If the rectangular plates of the capacitor have a width of 20 cm and a length of 40 cm, then the maximum electric charge in the capacitor is
A
2 µC
B
4 µC
C
8 µC
D
10 µC
2
GATE EE 2009
+2
-0.6
$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$\$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) evaluates to
A
-8
B
4
C
8
D
$$0$$
3
GATE EE 2008
+2
-0.6
A capacitor consists of two metal plates each $$500 \times 500\,\,m{m^2}$$ and spaced $$6$$ $$mm$$ apart. The space between the metal plates is filled with a glass plate of $$4$$ $$mm$$ thickness and a layer of paper of $$2$$ $$mm$$ thickness. The relative permittivity of the glass and paper are $$8$$ and $$2$$ respectively. Neglecting the fringing effect, the capacitance will be (Given that $${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,F/m$$ )
A
$$983.33$$ $$pF$$
B
$$1475$$ $$pF$$
C
$$6637.5$$ $$pF$$
D
$$9956.25$$ $$pF$$
4
GATE EE 2008
+2
-0.6
Two point charges $${Q_1} = 10\,\,\mu C$$ and $${Q_2} = 20\,\,\mu C$$ are placed at coordinates $$(1,1,0)$$ and $$\left( { - 1, - 1,0} \right)$$ respectively. The total electric flux passing through a plane $$z=20$$ will be
A
$$7.5\,\,\mu C$$
B
$$13.5\,\,\mu C$$
C
$$15.0\,\,\mu C$$
D
$$22.5\,\,\mu C$$
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