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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) (hatj+hatk+hati)`

D

`1/(sqrt2) (hati+hatk)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) If we take individual length for the purpose of calculating
the magnetic field in a 3-dimensional figure, then it will be
difficult.
Here, a smart choice is to divide the
loop into two loops. One loop is AD-
EFA in y-z plane and the other loop
will be ABCDA in the x-y plane.
We actually do not have any current
in the segment AD. By choosing the
loops, we find that in one loop we
have to take current from A to D and in the other one from
D to A. Hence, these two cancel out the effect of each other
as far as creating magnetic field at the concerned point is
considered.
The point (a,0,a) is in the X-Z plane.
The magnetic field due to current in ABCDA will be in
positive z direction . Due to symmetry, the y-components and
x-components will cancel out each other.
Similarly, the magnetic field due to current in ADEFA will
be in x direction.
`:. ` The resultant magnetic field will be `vecB=1/sqrt2(hati+hatj)`
Correct option is (d).
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