Question

The magnetic field at a distance of 2 cm from a current-carrying wire is 4 µT. Find the magnetic field at a distance of 1 cm from the wire.Group of answer choices2 µT4 µT6 µT8 µT

Answer 1

Given:

The magnetic field is

$B=\text{ 4 }\mu T$

when the distance is d = 2 cm.

To find the magnetic field when the distance is d' = 1 cm

Explanation:

The relation between magnetic field and distance is

$\begin{gathered} B=\frac{\mu_0I}{2\pi d} \\ B=\frac{k}{d} \end{gathered}$

Let the k be any arbitrary constant.

$\begin{gathered} k=\text{ Bd} \\ =4\text{ }\times2 \\ =8\text{ cm }\mu T \end{gathered}$

On substituting the values, the magnetic field will be

$\begin{gathered} B^{\prime}=\frac{k}{d} \\ =\frac{8\text{ cm }\mu T}{1\text{ cm}} \\ =\text{ 8 }\mu T \end{gathered}$

Final Answer: The magnetic field is 8 micro Tesla when the distance is 1 cm.