A solid non-magnetic conductor of circular cross section has its
| A solid non-magnetic conductor of circular cross section has its axis on z-axis and carries a uniformly distributed total current of 60 A in the az direction. If the radius of the conductor is 4 mm, find the magnetic flux density at ρ = 5 mm
A. 3.1 mT
B. 2.1 mT
C. 2.4 mT
D. 4.0 mT
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Right Answer is: C
SOLUTION
A solid non-magnetic circular conductor with the axis on Z-axis
Diagram
Radius r = 4 mm
= 4 × 10-3 m
Current I = 60 âz A
ρ = 5 mm = 5 × 10-3 m
\(\vec H\) at ρ = 5 mm is
\(\vec H = \frac{I}{{2\pi \rho }}{\hat a_\phi }\)
\(= \frac{{60}}{{2\pi \; \times \;5 \;\times \;{{10}^{ - 3}}}}{\hat a_\phi } = \frac{6}{\pi } \times {10^3}{\hat a_\phi }\)
Now, \(\vec B = {\mu _0}\vec H = \left( {4\pi \times {{10}^{ - 7}} \times \frac{6}{\pi } \times {{10}^3}} \right){\hat a_\phi }\)
\(\vec B = 24 \times {10^{ - 4}}\;{\hat a_\phi }T\)
⇒ B = 2.4 mT