First slide

Magnetic field due to a straight current carrying wire

Question

A very long straight cylindrical conductor of radius ‘a’ is carrying a steady current. If magnetic induction at the surface of a conductor is $B_{0}$ , what is the magnetic induction at a radial distance $r = \frac{a}{2}$ ?

Moderate

A

zero
B

$B_{0}$
C

$\frac{B_{0}}{4}$
D

$\frac{B_{0}}{2}$

Solution

$B_{0} = \frac{μ_{0} i}{2 π a}$
when $p \leq a, B = \frac{μ_{0}}{2} J r = \frac{μ_{0}}{2} (\frac{i}{π a^{2}}) r$
At $r = \frac{a}{2}, B = \frac{μ_{0}}{2}, \frac{i}{π a^{2}} . \frac{a}{2} = \frac{μ_{0} i}{4 π a} = \frac{B_{0}}{2}$

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