1
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
$$33$$ $$V$$
2
GATE EE 2001
+2
-0.6
The electric field $$\overrightarrow E$$ (in volts/metre) at the point $$(1, 1, 0)$$ due to a point charge of $$+1$$ $$\mu C$$ located at $$\left( { - 1,\,1,\,1} \right)$$ (coordinates in metres) is
A
$${{{{10}^{ - 6}}} \over {20\sqrt 5 \pi {\varepsilon _0}}}\left( {2i - k} \right)$$
B
$${{{{10}^{ - 6}}} \over {20\pi {\varepsilon _0}}}\left( {2i - k} \right)$$
C
$${{ - {{10}^{ - 6}}} \over {20\sqrt 5 \pi {\varepsilon _0}}}\left( {2i - k} \right)$$
D
$${{ - {{10}^{ - 6}}} \over {20\pi {\varepsilon _0}}}\left( {2i - k} \right)$$
3
GATE EE 2001
+2
-0.6
Given the potential function in free space to be $$V\left( x \right) = \left( {50{x^2} + 50{y^2} + 50{z^2}} \right)$$ volts, the magnitude (in volts /metre) and the direction of the electric field at a point $$\left( {1,\,\, - 1,\,\,1} \right),$$ where the dimensions are in metres, are
A
$$100\,\,\,\,;\left( {i + j + k} \right)$$
B
$$100/\sqrt 3 ;\,\,\left( {i - j + k} \right)$$
C
$$100\sqrt 3 ;\,\,\left[ {\left( { - i - j - k} \right) - \sqrt 3 } \right]$$
D
$$100\sqrt 3 ;\,\,\left[ {\left( { - i + j - k} \right) - \sqrt 3 } \right]$$
4
GATE EE 1997
Numerical
+2
-0
The capacitance of an isolated sphere of radius 10 cm in air is equal to _____ pF.