Question

Two parallel long wires carry currents \(i_{1}\) and \(i_{2}\) with \(i_{1}>i_{2}\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(10\ \mu\)T. If the direction of \(i_{2}\) is reversed then the field becomes \(30\ \mu\)T. The ratio \(\frac{i_{1}}{i_{2}}\)

• A. \(4\)
• B. \(3\)
• C. \(2\)
• D. \(1\)

Hint:

Midway the fields of the two wires add when currents are opposite and subtract when currents are in the same direction.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
At the midpoint each wire gives a field \(B\propto i\) with the same distance, so write \(B_{1}\propto i_{1}\) and \(B_{2}\propto i_{2}\).

Step 2: Form the Equations
Same direction: \(B_{1}-B_{2}=10\ \mu\)T.
Opposite direction: \(B_{1}+B_{2}=30\ \mu\)T.

Step 3: Solve
Adding gives \(B_{1}=20\ \mu\)T, and then \(B_{2}=10\ \mu\)T.

Step 4: Ratio
\(\dfrac{i_{1}}{i_{2}}=\dfrac{B_{1}}{B_{2}}=\dfrac{20}{10}=2\).

Final Answer:
The ratio i1/i2 is 2. \[ \boxed{\text{(C) }2} \]