GATE EE 2020 Set 1 — Question 65
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Electromagnetic Fields → Magnetic Circuits & Inductance → Self & Mutual Inductance
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Question
A conducting square loop of side length is placed at a distance of from a long straight wire carrying a current as shown below. The mutual inductance, in (rounded off to 2 decimal places), between the conducting loop and the long wire is _________.
Correct answer
138.1 to 139.2
Solution
The mutual inductance between a long straight wire and a square loop is defined as the ratio of the magnetic flux through the loop to the current in the wire: .
1.Magnetic Field due to the wire:
The magnetic field at a distance from an infinitely long straight wire carrying current is given by Ampere's Law:2.Magnetic Flux through the loop:
Consider a differential strip of width and height at a distance from the wire. The area of this strip is . The flux through the loop is:3.Mutual Inductance:
Given values:- Side length
- Distance
- Permeability of free space
4.Conversion to nH:
Rounding off to 2 decimal places, we get .Continue learning with Success Tracker
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