Consider an infinitely long straight cylindrical conductor of radius R with its axis along the Z-direction, which carries a current of 1A uniformly distributed over its cross-section. Which of the following statements is correct?
(where, r is the radial distance from the axis of the cylinder)
A. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{everywhere}}} \right)$$
B. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{everywhere}}} \right)$$
C. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = 0\,\,\,\left( {{\text{for }}r > R} \right)$$
D. $$\overrightarrow \nabla \times \overrightarrow {\bf{B}} = \frac{{{\mu _0}}}{{\pi {R^2}}}{\bf{\hat z}}\,\,\,\left( {{\text{for }}r > R} \right)$$
Answer: Option C
This Question Belongs to Engineering Physics >> Electromagnetic Theory
A. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} + y{\bf{\hat j}}} \right)$$
B. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} + {\bf{\hat J}}} \right)$$
C. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} - {\bf{\hat j}}} \right)$$
D. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} - y{\bf{\hat j}}} \right)$$
A. 0.033 μm
B. 0.330 μm
C. 3.300 μm
D. 33.000 μm
A. $${\bf{\hat z}}k$$
B. $${\bf{\hat x}}k\sin \alpha + {\bf{\hat y}}k\cos \alpha $$
C. $${\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\cos \alpha $$
D. $$ - {\bf{\hat z}}k$$
A. vp = vg
B. vp = $${\text{v}}_{\text{g}}^{\frac{1}{2}}$$
C. vp vg = c2
D. vg = $${\text{v}}_{\text{p}}^{\frac{1}{2}}$$
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