1
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
2
GATE ECE 2016 Set 2
+1
-0.3
A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity $$v=\widehat xv_x+\widehat zv_z$$. Given that B, m, q, vx and vz are all non-zero, which one of the following describes the eventual trajectory of the particle?
A
Helical motion in the $$\widehat z$$ direction.
B
Circular motion in the xy plane.
C
Linear motion in the $$\widehat z$$ direction.
D
Linear motion in the $$\widehat x$$ direction.
3
GATE ECE 2016 Set 2
Numerical
+1
-0
Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega$$ > 0 is a constant. When the vector magnitude $$\left| I \right|$$ is at its minimum value, the angle $$\theta$$ that I makes with the x axis (in degree, such that $$0\, \le \,0 \le \,180$$) is _________________
4
GATE ECE 2016 Set 3
+1
-0.3
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?
A
$$\nabla \bullet \,\mathop B\limits^ \to = \,0$$
B
$$\nabla \bullet \,\mathop D\limits^ \to = \,{\rho _v}$$
C
$$\nabla \, \times \,\mathop E\limits^ \to = \, - {{\partial \,\mathop B\limits^ \to \,} \over {\partial t}}$$
D
$$\nabla \, \times \,\mathop H\limits^ \to = \,\sigma \mathop E\limits^ \to + {{\partial \,\mathop D\limits^ \to \,} \over {\partial t}}$$
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