Question

The magnetic induction at the center $$O$$ in the figure shown is

Answer 1

Correct option is A. $$\dfrac {\mu_0i}{4}\left( \dfrac {1}{R_1}-\dfrac {1}{R_2}\right)$$

In the following figure, magnetic fields at $$O$$ due to sections $$1, 2, 3$$ and $$4$$ are considered as $$B_1, B_2, B_3$$ and $$B_4$$ respectively.

$$B_1=B_3=0$$

$$B_2=\dfrac{\mu_0}{4\pi}.\dfrac{\pi i}{R_1}\otimes $$

$$B_4=\dfrac{\mu_0}{4\pi}.\dfrac{\pi i}{R_2}\odot$$

So $$B_{net}=B_2-B_4\Rightarrow B_{net}=\dfrac{\mu_0i}{4}\left( \dfrac{1}{R_1}-\dfrac{1}{R_2}\right) \otimes $$