GATE ECE 2006 | GATE ECE Year Wise Previous Years Questions

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GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to

$$\mathrm P\times\nabla\times\mathrm P\;-\;\nabla^2\;\mathrm P$$

$$\nabla^2\;\mathrm P\;+\;\nabla\left(\nabla\cdot\mathrm P\right)$$

$$\nabla^2\;\mathrm P\;+\;\nabla\times\mathrm P$$

$$\nabla\left(\nabla\cdot\mathrm P\right)-\nabla^2\;\mathrm P\;$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

The electric field of an electromagnetic wave propagating in the positive z-direction is given by $$$E = {\widehat a_x}\sin \left( {\omega t - \beta z} \right) + {\widehat a_y}\sin \left( {\omega t - \beta z + \pi /2} \right)$$$

The wave is

linearly polarized in the z-direction

elliptically polarized

left-hand circularly polarized

right-hand circularly polarized

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

A medium of relative permittivityb $${\varepsilon _r} = 2$$ forms an interface with free-space. A point source of electromagnetic energy is located in the medium at a depth of $$1$$ meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the interface is given by

$$2\pi \,{m^2}$$

$${\pi ^2}\,{m^2}$$

$$\pi /2\,{m^2}$$

$$\pi \,{m^2}$$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.3

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to

$$P \times \nabla \times P - {\nabla ^2}P$$

$${\nabla ^2}P + \nabla \left( {\nabla .P} \right)$$

$${\nabla ^2}P + \nabla \times P$$

$$\nabla \left( {\nabla .P} \right) - {\nabla ^2}P$$

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2023