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 (\(\mu _{0}\) = permeability of free space)
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 (\(\mu _{0}\) = permeability of free space)
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For opposite currents the fields at the midpoint add; use B equals mu0 I over 2 pi d for each wire.
Updated On: Nov 12, 2026
- \(\frac{5\mu _{0}}{2\pi }\)
- \(\frac{3\mu _{0}}{4\pi }\)
- \(\frac{2\mu _{0}}{\pi }\)
- \(\frac{5\mu _{0}}{6\pi }\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
A long straight wire gives \(B=\frac{\mu_{0}I}{2\pi d}\).
With opposite currents, the fields at the midpoint are in the same direction, so they add.
Step 2: Distance
The midpoint is \(d=\frac{3}{2}=1.5\) m from each wire.
Step 3: Calculation
\(B=\frac{\mu_{0}}{2\pi\times1.5}(3+4.5)=\frac{7.5\mu_{0}}{3\pi}=\frac{5\mu_{0}}{2\pi}\)
Step 4: Compare the options
This is option (A).
Final Answer:
The resultant field is 5 mu0 over 2 pi. \[ \boxed{\text{(A) }\dfrac{5\mu_{0}}{2\pi}} \]
A long straight wire gives \(B=\frac{\mu_{0}I}{2\pi d}\).
With opposite currents, the fields at the midpoint are in the same direction, so they add.
Step 2: Distance
The midpoint is \(d=\frac{3}{2}=1.5\) m from each wire.
Step 3: Calculation
\(B=\frac{\mu_{0}}{2\pi\times1.5}(3+4.5)=\frac{7.5\mu_{0}}{3\pi}=\frac{5\mu_{0}}{2\pi}\)
Step 4: Compare the options
This is option (A).
Final Answer:
The resultant field is 5 mu0 over 2 pi. \[ \boxed{\text{(A) }\dfrac{5\mu_{0}}{2\pi}} \]
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