Question

In the given figure, what is the magnetic field at the point ${}^{\prime }{O}^{\prime }$ ?

• A. $\frac{{\mu }_{0}I}{4\pi r}+\frac{{\mu }_{0}I}{2\pi r}$
• B. $\frac{{\mu }_{0}I}{4\pi r}$
• C. $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{2\pi r}$
• D. $\frac{{\mu }_{0}I}{4r}-\frac{{\mu }_{0}I}{4\pi r}$

Answer 1

The correct option is C $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{2\pi r}$

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 $B-1=\frac{{\mu }_{o}I}{4r}$ ,by right hand thumb rule its outward to plane

Magnetic field due to semi infinite wire at r distance is $B_2=\frac{{\mu }_{0}I}{4\pi r}$. by right hand thumb rule its outward to plane

total magnetic field =$B_1+B_2=\frac{{\mu }_{o}I}{4r}+\frac{{\mu }_{o}I}{4\pi r}$