First slide

Magnetic field due to a straight current carrying wire

Question

A long wire is bent into the shape PQRST as shown in the following figure with QRS being a semicircle with centre O and radius r metre. A current of I ampere flows through it in the direction P $\to$ Q $\to$ R $\to$ S $\to$ T . Then the magnetic induction at the point O of the figure in vacuum is

Moderate

A

$μ_{0} (\frac{I}{2 π r} - \frac{I}{4 r})$
B

$μ_{0} (\frac{I}{2 r})$
C

$μ_{0} (\frac{I}{2 π r} + \frac{I}{4 r})$
D

$μ_{0} (\frac{I}{4 r})$

Solution

magnetic field due to each of half infinite wire is $\frac{μ_{0} I}{4 π r}$ and int he same downward direction and field due to semi circle is also downward and has a value $\frac{μ_{0} I}{4 r}$

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