GATE ECE 2016 Set 3 | Maxwell Equations Question 8 | Electromagnetics

GATE ECE 2016 Set 3

MCQ (Single Correct Answer)

-0.3

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

$$\nabla \bullet \,\mathop B\limits^ \to = \,0$$

$$\nabla \bullet \,\mathop D\limits^ \to = \,{\rho _v}$$

$$\nabla \, \times \,\mathop E\limits^ \to = \, - {{\partial \,\mathop B\limits^ \to \,} \over {\partial t}}$$

$$\nabla \, \times \,\mathop H\limits^ \to = \,\sigma \mathop E\limits^ \to + {{\partial \,\mathop D\limits^ \to \,} \over {\partial t}}$$

GATE ECE 2016 Set 2

Numerical

-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 _________________

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GATE ECE 2016 Set 2

MCQ (Single Correct Answer)

-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, v_x and v_z are all non-zero, which one of the following describes the eventual trajectory of the particle?

Helical motion in the $$\widehat z$$ direction.

Circular motion in the xy plane.

Linear motion in the $$\widehat z$$ direction.

Linear motion in the $$\widehat x$$ direction.

GATE ECE 2016 Set 1

Numerical

-0

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m² , −4 nC/m² and ρ_s ,respectively. The value of ρ_s (nC/m²) required to ensure that the electric flux density $$\overrightarrow D=\overrightarrow0$$ at radius 10 m is _________.

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