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A non - popular loop of conducting wire ...

A non - popular loop of conducting wire carrying a current `I` is placed as shown in the figure . Each of the straighrt sections of the loop is of the length ` 2a`. The magnetic field due to this loop at the point `P(a, 0 ,a)` points in the direction

A

`1/sqrt2(-hatj+hatk)`

B

`1/sqrt3(-hatj+hatk+hati)`

C

`1/sqrt3(hati+hatk-hat5)`

D

`1/sqrt2(hati+hatk)`

Text Solution

Verified by Experts

The correct Answer is:
D
The magnetic field at `P(a,0)` due to the loop is equal to the vector sum of the magnetic field produced by loops `ABCDA` and `AFEBA` as shown in figure.
Magnetic field due loop `ABCDA` will be along `hati` and due to loop `AFEBA` along `hatk`.Magnitude of magnetic field due to both the loops will be equal.Therefore, direction of resultant magnetic field at `P` will be `1/sqrt2(hati+hatk)`
This is a common practice, when by assuming equal current in opposite directions in an imaginary wire (here `AB`).loops are completed and solution becomes easy.
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