1
GATE ECE 2015 Set 3
Numerical
+2
-0
A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner is doubled, the capacitance per unit length (in pF/m) is _____.
2
GATE ECE 2014 Set 4
+2
-0.6
If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\right)\widehat{\mathrm z}$$

is the electric field in a source free region, a valid expression for the electrostatic potential is

A
xy3 - yz2
B
2xy3 - xyz2
C
y3 + xyz2
D
2xy3 - 3xyz2
3
GATE ECE 2014 Set 4
Numerical
+2
-0
The electric field (assumed to be one-dimensional) between two points A and B is shown. Let $$\psi_A$$ and $$\psi_B$$ be the electrostatic potentials at A and B, respectively. The value of $$\psi_A$$ − $$\psi_B$$ in Volts is ________.
4
GATE ECE 2014 Set 3
Numerical
+2
-0
Given the vector $$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right){\widehat{\mathrm a}}_\mathrm y$$\$ where $${\widehat{\mathrm a}}_\mathrm x$$ , $${\widehat{\mathrm a}}_\mathrm y$$ denote unit vectors along x, y directions, respectively. The magnitude of curl of A is ________