Question

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?

0.01 T
0.05 T
0.1 T
0.2 T

Answer 1

The magnetic field around a long straight wire carrying an electric current can be calculated using Ampère's Law. The magnitude of the magnetic field (B) at a distance (r) from the wire is given by the formula:

\[
B = \frac{\mu_0 I}{2 \pi r}
\]

where \( \mu_0 \) is the permeability of free space and \( I \) is the current through the wire.

From the formula, you can see that the magnetic field is inversely proportional to the distance from the wire. This means:

\[
B_1 r_1 = B_2 r_2
\]

Given:
- At \( r_1 = 0.02 \) m, \( B_1 = 0.1 \) T.
- We want to find \( B_2 \) at \( r_2 = 0.01 \) m.

Using the ratio:

\[
B_1 r_1 = B_2 r_2
\]

Substituting the known values:

\[
0.1 \times 0.02 = B_2 \times 0.01
\]

\[
0.002 = B_2 \times 0.01
\]

Now, solve for \( B_2 \):

\[
B_2 = \frac{0.002}{0.01}
\]

\[
B_2 = 0.2 \text{ T}
\]

Thus, the magnitude of the magnetic field 0.01 m from the wire is **0.2 T**.