1
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +𝑄 is placed at a distance of 𝑑 from both sheets. The net force on the charge is $$\frac{Q^2}{4{\mathrm{πε}}_0}\frac{\overrightarrow K}{d^2}$$ , where $$\overrightarrow K$$ is given by GATE EE 2015 Set 2 Electromagnetic Fields - Electrostatics Question 30 English
A
0
B
$$-\frac14\widehat i\;-\frac14\widehat j$$
C
$$-\frac18\widehat i\;-\frac18\widehat j$$
D
$$\frac{1-2\sqrt2}{8\sqrt2}\widehat i\;+\frac{1-2\sqrt2}{8\sqrt2}\widehat j$$
2
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Two semi-infinite dielectric regions are separated by a plane boundary at y = 0. The dielectric constants of region 1 (y< 0) and region 2 (y>0) are 2 and 5, respectively. Region 1 has uniform electric field $$\overrightarrow E=3{\widehat a}_x\;+\;4{\widehat a}_y\;+\;2{\widehat a}_z$$, where $${\widehat a}_x$$, $${\widehat a}_y$$, and $${\widehat a}_Z$$ are unit vectors along the x, y and z axes, respectively. The electric field in region 2 is
A
$$3{\widehat a}_x\;+\;1.6{\widehat a}_y\;+\;2{\widehat a}_z$$
B
$$1.2{\widehat a}_x\;+\;4{\widehat a}_y\;+\;2{\widehat a}_z$$
C
$$1.2{\widehat a}_x\;+\;4{\widehat a}_y\;+\;0.8{\widehat a}_z$$
D
$$3{\widehat a}_x\;+\;10{\widehat a}_y\;+\;0.8{\widehat a}_z$$
3
GATE EE 2015 Set 2
Numerical
+1
-0
A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of μ0 is $$4\mathrm\pi\times10^{-7}$$ in SI unit. If a uniform magnetic field intensity $$\overrightarrow H=10^7\;\widehat z\;A/m$$ is applied, then the peak value of the induced voltage, Vturn ( in Volts), is _________. GATE EE 2015 Set 2 Electromagnetic Fields - Time Varying Fields Question 10 English
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4
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Given $$f\left( z \right) = g\left( z \right) + h\left( z \right),$$ where $$f,g,h$$ are complex valued functions of a complex variable $$z.$$ Which ONE of the following statements is TRUE?
A
If $$f(z)$$ is differentiable at $${z_0},$$ then $$g(z)$$ & $$h(z)$$ are also differentiable at $${z_0}.$$
B
If $$g(z)$$ & $$h(z)$$ are differentiable at $${z_0},$$ then $$f(z)$$ is also differentiable at $${z_0}.$$
C
If $$f(z)$$ is continuous at $${z_0},$$ then it is differentiable at $${z_0}.$$
D
If $$f(z)$$ is differentiable at $${z_0},$$ then so are its real and imaginary parts.
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