Two wires are bent (shown as joint-circle) with radius r (in xy plane). The upper half has resistance of 2RΩ and the lower half of RΩ . A current I is passed into circle as shown. The magnetic field at centre is:

Question

Two wires are bent (shown as joint-circle) with radius r (in xy plane). The upper half has resistance of 2RΩ and the lower half of RΩ . A current I is passed into circle as shown. The magnetic field at centre is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-sc0q2hmi1fcaynag.jpg" /> (A) ((μ )0 I/r)( hatk) (B) ((μ )0 I/2 r)( hatk) (C) zero (D) ((μ )0 I/12 r)( hatk)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-sc0q2hmi1fcapnuq.jpg" /> Magnetic field at centre, BC=((μ )0/4 r)[((2 I/3)) - ((I/3))]=((μ )0 I/12 r) outward so direction is along hatk .

Q. Two wires are bent (shown as joint-circle) with radius $r$ (in $x y$ plane). The upper half has resistance of $2 R Ω$ and the lower half of $R Ω$ . A current $I$ is passed into circle as shown. The magnetic field at centre is :

$\frac{( μ ) _{0} I}{r} (\hat{k})$

$\frac{( μ ) _{0} I}{2 r} (\hat{k})$

zero

$\frac{( μ ) _{0} I}{12 r} (\hat{k})$

Magnetic field at centre,
$B_{C} = \frac{( μ ) _{0}}{4 r} [(\frac{2 I}{3}) - (\frac{I}{3})] = \frac{( μ ) _{0} I}{12 r}$
outward so direction is along $\hat{k}$ .

Q. Two wires are bent (shown as joint-circle) with radius r (in xy plane). The upper half has resistance of 2RΩ and the lower half of RΩ . A current I is passed into circle as shown. The magnetic field at centre is :

r(μ)0​I​(k^)

2r(μ)0​I​(k^)