1
GATE ECE 2014 Set 3
Numerical
+2
-0
Given the vector $$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right){\widehat{\mathrm a}}_\mathrm y$$\$ where $${\widehat{\mathrm a}}_\mathrm x$$ , $${\widehat{\mathrm a}}_\mathrm y$$ denote unit vectors along x, y directions, respectively. The magnitude of curl of A is ________
2
GATE ECE 2012
+2
-0.6
An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$

The magnetic field at a distance r from the center of the wire is proportional to

A
r for r < a and 1/r2 for r > a
B
0 for r < a and 1/r for r > a
C
r for r < a and 1/r for r > a
D
0 for r < a and 1/r2 for r > a
3
GATE ECE 2012
+2
-0.6
An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$.

A hole of radius b (b < a) is now drilled along the length of the wire at a distance d from the center of the wire as shown below.

The magnetic field inside the hole is

A
uniform and depends only on d
B
uniform and depends only on b
C
uniform and depends on both b and d
D
non uniform
4
GATE ECE 2010
+2
-0.6
If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_\mathrm y$$ then $$\oint\overrightarrow{\mathrm A}.\overrightarrow{\mathrm d}\mathcal l$$ over the path shown in the figure is
A
$$0$$
B
$$\frac2{\sqrt3}$$
C
1
D
$$2\sqrt3$$
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