91Ó°ÊÓ

#tag_title#Step 2: Find the magnetic field with only I wire active#tag_content# When the wire carrying current 2I is switched off, only the wire carrying current I will generate a magnetic field. Since the configuration remains symmetric, we can still use the simplified formula for the magnetic field generated by a current-carrying wire at the midpoint: \(B_I = \frac{\mu_0 * I}{4\pi * d}\) #tag_title#Step 3: Compare the magnetic field magnitudes in both situations#tag_content# Now, we need to compare the magnetic field B with both wires active and the magnetic field \(B_I\) with only the I wire active, as found in the previous step. To do this, we will divide the two magnetic field magnitudes: \(\frac{B_I}{B} = \frac{\frac{\mu_0 * I}{4\pi * d}}{\frac{\mu_0 * I}{4\pi * d} + \frac{\mu_0 * 2I}{4\pi * d}}\) Simplifying the expression, we get: \(\frac{B_I}{B} = \frac{1}{1 + 2}\) \(\frac{B_I}{B} = \frac{1}{3}\) This means that the magnetic field magnitude at the midpoint when the 2I wire is switched off will be one-third of the initial magnetic field magnitude. Therefore, the field when the 2I wire is switched off will be: \(B_I = \frac{B}{3}\) However, this option is not present in the given choices. It indicates that the problem statement or given options may have an error.