Question

Two parallel wires of equal lengths are separated by a distance of \(3\) m from each other. The currents flowing through first and second wire is \(3\) A and \(4.5\) A respectively in opposite directions. The resultant magnetic field at mid point of both the wires is (\(μ_0\)=permeability of free space)

• A. \(\frac{μ_0}{2π}\)
• B. \(\frac{5μ_0}{2π}\)
• C. \(\frac{7μ_0}{2π}\)
• D. \(\frac{9μ_0}{2π}\)

Hint:

At the midpoint, fields of opposite currents point the same way and add.

Answer 1

The Correct Option is B

Step 1: Use the right hand rule:
For wires carrying currents in opposite directions, at any point in the plane between them both fields point out of (or into) the page.

Step 2: Compute with a common factor:
$B=\dfrac{\mu_0}{2\pi r}(I_1+I_2)=\dfrac{\mu_0}{2\pi(1.5)}(3+4.5)$.

Step 3: Simplify:
$\dfrac{7.5}{1.5}=5$, so $B=\dfrac{5\mu_0}{2\pi}$. Option B.

Final Answer:
The fields from the two opposite currents add to 5 mu0/(2 pi). \[ \boxed{\text{(B) }\dfrac{5\mu_0}{2\pi}} \]