1
GATE EE 2015 Set 1
Numerical
+2
-0
A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.
2
GATE EE 2015 Set 2
+2
-0.6
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +𝑄 is placed at a distance of 𝑑 from both sheets. The net force on the charge is $$\frac{Q^2}{4{\mathrm{πε}}_0}\frac{\overrightarrow K}{d^2}$$ , where $$\overrightarrow K$$ is given by
A
0
B
$$-\frac14\widehat i\;-\frac14\widehat j$$
C
$$-\frac18\widehat i\;-\frac18\widehat j$$
D
$$\frac{1-2\sqrt2}{8\sqrt2}\widehat i\;+\frac{1-2\sqrt2}{8\sqrt2}\widehat j$$
3
GATE EE 2014 Set 3
+2
-0.6
A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of $$+32{\mathrm{πε}}_0\sqrt2$$ columbs is placed at coordinate (0, 0, 2). $${\mathrm\varepsilon}_0$$ is the permittivity of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. At the coordinate $$\left(\sqrt2,\sqrt2,0\right)$$, the electric field vector $$\overrightarrow E$$ (Newtons/Columb) will be
A
$$2\sqrt2\widehat K$$
B
$$-2\widehat K$$
C
$$2\widehat K$$
D
$$-2\sqrt2\widehat K$$
4
GATE EE 2013
+2
-0.6
A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of $$E=6{\widehat a}_x+8{\widehat a}_y$$ kV /mm. The relative permittivity of the dielectric material is equal to 2. The value of constant $$\varepsilon_0$$ is $$8.85\times10^{-12}\;F/m$$ . The energy stored in the dielectric in Joules is
A
$$8.85\times10^{-11}$$
B
$$8.85\times10^{-5}$$
C
88.5
D
885
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Medical
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