Shown in the figure is a conductor carrying a current I. The magnetic field intensity at the point O (common centre of all the three arcs) is :-

Question

Shown in the figure is a conductor carrying a current I. The magnetic field intensity at the point O (common centre of all the three arcs) is :- <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-toyluqjivjksiynq.jpg" /> (A) (5 μ 0 Iθ /24 π r) (B) (μ 0 Iθ /24 π r) (C) (11 μ 0 Iθ /24 π r) (D) zero

Tardigrade Admin · Accepted Answer

since, magnetic field at the centre of an arc is equal to B=(μ o I/4 π r)θ Hence, net B=(μ 0 I/4 π )[(1/r) - (1/2 r) + (1/3 r)]θ =(5 μ 0 Iθ /24 π r)

Q. Shown in the figure is a conductor carrying a current $I .$ The magnetic field intensity at the point $O$ (common centre of all the three arcs) is :-

$\frac{5 μ _{0} I θ}{24 π r}$

$\frac{μ _{0} I θ}{24 π r}$

$\frac{11 μ _{0} I θ}{24 π r}$

zero

since, magnetic field at the centre of an arc is equal to
$B = \frac{μ _{o} I}{4 π r} θ$
Hence, net $B = \frac{μ _{0} I}{4 π} [\frac{1}{r} - \frac{1}{2 r} + \frac{1}{3 r}] θ$
$= \frac{5 μ _{0} I θ}{24 π r}$

Q. Shown in the figure is a conductor carrying a current I. The magnetic field intensity at the point O (common centre of all the three arcs) is :-

24πr5μ0​Iθ​

24πrμ0​Iθ​

24πr11μ0​Iθ​