1
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
$$0$$
2
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
$$9956.25$$ $$pF$$
3
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
$$22.5\,\,\mu C$$
4
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
$${1 \over {4\pi {\varepsilon _0}}}{{QR} \over {{r^3}}}$$
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