1
GATE ECE 2024
+1
-0.33

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vector fields $\vec{F}_1 = A(\hat{i}y + \hat{j}x)$ and $\vec{F}_2 = A(\hat{i}y − \hat{j}x)$?

A

Both $\vec{F}_1$ and $\vec{F}_2$ are electrostatic fields.

B

Only $\vec{F}_1$ is an electrostatic field.

C

Only $\vec{F}_2$ is an electrostatic field.

D

Neither $\vec{F}_1$ nor $\vec{F}_2$ is an electrostatic field.

2
GATE ECE 2022
+1
-0.33

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + $$\pi$$/2). The displacement current (in Amperes) through the capacitor is __________.

A
2sin(t)
B
2sin(t + $$\pi$$)
C
2sin(t + $$\pi$$/2)
D
0
3
GATE ECE 2022
Numerical
+1
-0.33

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D$$, is given by

$$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarrow j + x{y^2}\overrightarrow k )$$ C/m2,

where, $$\overrightarrow i$$, $$\overrightarrow j$$, $$\overrightarrow k$$ are the unit vectors along x-axis, y-axis, and z-axis, respectively. Consider a cubical region R centered at the origin with each side of length 1 m, and vertices at ($$\pm$$ 0.5 m, $$\pm$$ 0.5 m, $$\pm$$ 0.5 m). The electric charge enclosed within R is __________ C (rounded off to two decimal places).

4
GATE ECE 2017 Set 2
+1
-0.3
Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are Va and Ea , and that on S2 are Vb and Eb, respectively, which of the following is CORRECT?

A
Va = Vb and Ea < Eb
B
Va > Vb and Ea > Eb
C
Va = Vb and Ea > Eb
D
Va > Vb and Ea = Eb
EXAM MAP
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