the magnetic field 0.02 m from a wire is 0.1 t. what is the magnitude of the magnetic field 0.01 m from the…

the magnetic field 0.02 m from a wire is 0.1 t. what is the magnitude of the magnetic field 0.01 m from the same wire?\n0.01 t\n0.05 t\n0.1 t\n0.2 t
Answer
Explanation:
Step1: Recall magnetic - field formula
The magnetic field $B$ due to a long - straight wire is given by $B=\frac{\mu_0I}{2\pi r}$, where $\mu_0$ is the permeability of free space, $I$ is the current in the wire, and $r$ is the distance from the wire. For a given wire (constant $I$), $B$ is inversely proportional to $r$, i.e., $B_1r_1 = B_2r_2$.
Step2: Substitute the given values
We are given $B_1 = 0.1\ T$, $r_1=0.02\ m$, and $r_2 = 0.01\ m$. Using the relation $B_1r_1 = B_2r_2$, we can solve for $B_2$. Rearranging the formula gives $B_2=\frac{B_1r_1}{r_2}$. Substitute the values: $B_2=\frac{0.1\ T\times0.02\ m}{0.01\ m}$. $B_2 = 0.2\ T$.
Answer:
0.2 T