1
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.
2
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 _________________
3
GATE ECE 2016 Set 1
Numerical
+1
-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 ρs ,respectively. The value of ρs (nC/m2) required to ensure that the electric flux density $$\overrightarrow D=\overrightarrow0$$ at radius 10 m is _________.
4
GATE ECE 2015 Set 2
Numerical
+1
-0
In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.