Question
The magnetic field at a distance $$r$$ from a long wire carrying current $$i$$ is $$0.4\,T.$$ The magnetic field at a distance $$2r$$ is
A.
$$0.2\,T$$
B.
$$0.8\,T$$
C.
$$0.1\,T$$
D.
$$1.6\,T$$
Answer :
$$0.2\,T$$
Solution :
Magnetic field due to a long current carrying wire at distance $$r$$ at point $$P$$ is given by
$$B = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{2i}}{r}$$
So, $$B \propto \frac{1}{r}$$
when $$r$$ is doubled, the magnetic field becomes halved.
i.e., $$B' = \frac{B}{2} \Rightarrow B' = \frac{{0.4}}{2} = 0.2\,T$$
Magnetic field due to a long current carrying wire at distance $$r$$ at point $$P$$ is given by
$$B = \frac{{{\mu _0}}}{{4\pi }} \cdot \frac{{2i}}{r}$$
So, $$B \propto \frac{1}{r}$$
when $$r$$ is doubled, the magnetic field becomes halved.
i.e., $$B' = \frac{B}{2} \Rightarrow B' = \frac{{0.4}}{2} = 0.2\,T$$