Question

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

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

Answer 1

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

Answer is C.
Circular wire produces magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;$B=\frac{{\mu }_{0}I}{2r}where,{\mu }_0=4\pi \times {10}^{-7}N/A-m$.
since we have semicircle, we put 1/2 in front of our formula.
Therefore, the formula becomes $\frac{1}{2}\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_{0}I}{4r}N/A-m$.
Also, there is curved staight wire in the figure, the magnetic field is given as $\frac{{\mu }_{0}I}{4\pi r}$.
Therefore, the magnetic field at the point 'O' is $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{4\pi r}$.