First slide

Magnetic field due to a current carrying circular ring

Question

A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is

Moderate

A

$\frac{μ_{0} i}{4 r}$
B

$\frac{μ_{0} i}{2 r}$
C

$\frac{μ_{0} i}{2 π r} (π + 1)$
D

$\frac{μ_{0} i}{2 π r} (π - 1)$

Solution

The given circuit can be considered as follows
$\begin{array}{l} B_{loop} = \frac{μ_{0} i}{2 r} ⊙ \\ B_{conductor} = \frac{μ_{0} i}{2 πr} ⊙ \\ B_{net} = \frac{μ_{0} i}{2 πr} (π + 1) ⊙ \end{array}$

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