MCQ
The magnetic field at point, point $P$ will be :-
- A$\frac{{{\mu _0}i}}{{8\pi l}}$
- ✓$\frac{{{\mu _0}i}}{{8\sqrt 3 \pi l}}$
- C$\frac{{{\mu _0}i}}{{4\pi l}}$
- D$\frac{{{\mu _0}i}}{{4\sqrt 3 \pi l}}$
✓
Answer
Correct option: B.
$\frac{{{\mu _0}i}}{{8\sqrt 3 \pi l}}$
b
${{{\text{B}}_{\text{p}}} = \frac{{{\mu _0}{\text{i}}}}{{4\pi {\text{d}}}}\left( {\sin {\theta _1} + \sin {\theta _2}} \right)}$
${{{\text{B}}_{\text{p}}} = \frac{{{\mu _0}{\text{i}}}}{{4\pi {\text{d}}}}\left( {\sin {\theta _1} + \sin {\theta _2}} \right)}$
${({\text{d}} = \sqrt 3 \ell }$ ${{\theta _1} = 0)}$
${ \Rightarrow \frac{{{\mu _0}{\text{i}}}}{{4\pi \sqrt 3 \ell }}\left( {\sin 0 + \frac{\ell }{{2\ell }}} \right)}$
${ \Rightarrow \frac{{{\mu _0}{\text{i}}}}{{4\sqrt 3 \pi l}}\left( {\frac{1}{2}} \right)}$
${\boxed{{{\text{B}}_{\text{p}}} \Rightarrow \frac{{{\mu _0}{\text{i}}}}{{8\sqrt 3 \pi l}}}}$
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