First slide
Magnetic field due to a current carrying circular ring
Question

A portion of a conductive wire is bent in the form of a semicircle of radius r as shown below in fig. At the centre of semicircle, the magnetic induction will be

Easy
Solution

The straight part will not contribute magnetic field at the centre of the semicircle because every element of the straight part will be 0° or 180°with the line joining the centre and the element. Due to circular portion, the field is
12μ0i2r=μ0i4r
Hence total field at O =μ0i4r tesla 

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