Question

A current in a wire increases from 2 A to 6 A. How will the magnetic field 0.01 m from the wire change?

It increases to four times its original value.
It increases to three times its original value.
It decreases to one-fourth its original value.
It decreases to one-third its original value.

Answer 1

The magnetic field \( B \) around a long straight wire carrying a current \( I \) is given by Ampère's law through the formula:

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

where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (a constant),
- \( I \) is the current through the wire,
- \( r \) is the distance from the wire.

In this case, the distance \( r = 0.01 \) m remains constant as the current changes from \( 2 \) A to \( 6 \) A.

To find out how the magnetic field changes with the increase in current, we can set up a ratio of the magnetic field at the two different currents:

\[
\frac{B_2}{B_1} = \frac{\frac{\mu_0 I_2}{2 \pi r}}{\frac{\mu_0 I_1}{2 \pi r}} = \frac{I_2}{I_1}
\]

Substituting the values of the currents:

\[
\frac{B_2}{B_1} = \frac{6\, \text{A}}{2\, \text{A}} = 3
\]

This means the magnetic field at 6 A is three times the magnetic field at 2 A.

Therefore, the change in the magnetic field when the current increases from 2 A to 6 A is that it **increases to three times its original value**.

Thus, the correct answer is:

**It increases to three times its original value.**