Question

A wire carrying current I and other parallel wire carrying current 2I in the same direction produces a magnetic field B at the midpoint between them. Then the magnitude of field at the same point, when the 2I wire is switched off

• A. B/2
• B. 2 B
• C. B
• D. 4 B

Hint:

Parallel currents in the same direction subtract fields at the midpoint. Since $2I - I = I$, turning off the $2I$ wire leaves the field of $I$ alone, keeping the magnitude identical!

Answer 1

The Correct Option is C

Step 1: Concept
The magnetic field at a distance r from a long straight wire carrying current I is given by $B = \frac{\mu_{0}I}{2\pi r}$. The direction of the field is determined by the right-hand thumb rule.

Step 2: Meaning
Let the distance between the two parallel wires be $2d$. The midpoint is at a distance $d$ from both wires. Since the currents flow in the same direction, their magnetic fields at the midpoint oppose each other.

Step 3: Analysis
The magnetic field due to the first wire is $B_{1} = \frac{\mu_{0}I}{2\pi d}$ (pointing in one direction). The magnetic field due to the second wire is $B_{2} = \frac{\mu_{0}(2I)}{2\pi d} = 2B_{1}$ (pointing in the opposite direction). The net magnetic field $B$ is the difference between them: $B = B_{2} - B_{1} = 2B_{1} - B_{1} = B_{1}$. When the 2I wire is switched off, $B_{2}$ becomes zero.

Step 4: Conclusion
The remaining magnetic field at the midpoint is solely due to the first wire, which is $B_{1}$. Since $B = B_{1}$, the magnitude of the field remains $B$.

Final Answer: (C)