A long cylindrical kept along Z-axis carries a current density $${\bf{\hat J}} = {J_0}r{\bf{\hat k}},$$ where $${J_0}$$ is a constant and r is the radial distance from the axis of the cylinder. The magnetic induction $$\overrightarrow {\bf{B}} $$ inside the conductor at a distance d from the axis of the cylinder is
A. $${\mu _0}{J_0}\hat \phi $$
B. $$ - \frac{{{\mu _0}{J_0}d}}{2}\hat \phi $$
C. $$\frac{{{\mu _0}{J_0}{d^2}}}{3}\hat \phi $$
D. $$ - \frac{{{\mu _0}{J_0}{d^3}}}{4}\hat \phi $$
Answer: Option C
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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