1
GATE ECE 2011
+1
-0.3

Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point inside S, with $$\widehat n$$ the unit normal on S, the value of the integral is

A
3 V
B
5 V
C
10 V
D
15 V
2
GATE ECE 2009
+1
-0.3
Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin?
A
x, y, z components
B
x, y components
C
y, z components
D
x, z components
3
GATE ECE 2007
+1
-0.3
If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H$$, the current density $$\overrightarrow J$$ and the electric flux density $$\overrightarrow D$$ are related by
A
$$\int\!\!\!\int\limits_S {\overrightarrow H } .d\overrightarrow s = \oint\limits_C {\left( {\overrightarrow J + {{\partial \overrightarrow D } \over {\partial t}}} \right)} .d\overrightarrow l$$
B
C
D
$$\oint\limits_C {\overrightarrow H } .d\overrightarrow l = \int\!\!\!\int\limits_S {\left( {\overrightarrow J + {{\partial \overrightarrow D } \over {\partial t}}} \right)} .d\overrightarrow s$$
4
GATE ECE 2006
+1
-0.3
$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to
A
$$\mathrm P\times\nabla\times\mathrm P\;-\;\nabla^2\;\mathrm P$$
B
$$\nabla^2\;\mathrm P\;+\;\nabla\left(\nabla\cdot\mathrm P\right)$$
C
$$\nabla^2\;\mathrm P\;+\;\nabla\times\mathrm P$$
D
$$\nabla\left(\nabla\cdot\mathrm P\right)-\nabla^2\;\mathrm P\;$$
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