Single Choice

In the given figure, what is the magnetic field at the point $$'O'$$ ?

A$$\displaystyle \frac {\mu_{0}I}{4\pi r} + \frac {\mu_{0}I}{2\pi r}$$
B$$\displaystyle \frac {\mu_{0}I}{4\pi r}$$
C$$\displaystyle \frac {\mu_{0}I}{4r} + \frac {\mu_{0}I}{2\pi r}$$
Correct Answer
D$$\displaystyle \frac {\mu_{0}I}{4r} - \frac {\mu_{0}I}{4\pi r}$$

Solution

The magnetic filed due the the straight fir passing through o is zero ,because here angle between current carrying wire and the o is zero.
now magnetic field due to semicircular wire is $$B-1=\dfrac{\mu_oI}{4r}$$ ,by right hand thumb rule its outward to plane
Magnetic field due to semi infinite wire at r distance is $$B_2=\dfrac{\mu_0I}{4\pi r}$$. by right hand thumb rule its outward to plane
total magnetic field =$$B_1+B_2=\dfrac{\mu_oI}{4r}+\dfrac{\mu_oI}{4\pi r}$$


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