The wire in the figure carries a current i and consists of a circular arc of radius R and central angle (π /2) rad, and two straight sections whose extensions intersect the center C of the arc. The magnetic field B that the current produces at C is

Question

The wire in the figure carries a current i and consists of a circular arc of radius R and central angle (π /2) rad, and two straight sections whose extensions intersect the center C of the arc. The magnetic field B that the current produces at C is (A)  | B |=(μ0i/8R) into the plane of the figure (B)  | B |=(μ0i/8R) out of the plane of the figure (C)  | B |=(μ0i/8π R) in to the plane of the figure (D)  | B |=(μ0i/8π R) out of the plane of the figure

Tardigrade Admin · Accepted Answer

Magnetic field at C is B=(1/4) (due to whole circle) =(1/4)( (μ 0i/2R) )=(μ0i/8R)

Q. The wire in the figure carries a current $i$ and consists of a circular arc of radius $R$ and central angle $\frac{π}{2}$ rad, and two straight sections whose extensions intersect the center $C$ of the arc. The magnetic field $B$ that the current produces at $C$ is

$∣ B ∣ = \frac{μ _{0} i}{8 R}$ into the plane of the figure

$∣ B ∣ = \frac{μ _{0} i}{8 R}$ out of the plane of the figure

$∣ B ∣ = \frac{μ _{0} i}{8 π R}$ in to the plane of the figure

$∣ B ∣ = \frac{μ _{0} i}{8 π R}$ out of the plane of the figure

Magnetic field at $C$ is
$B = \frac{1}{4}$ (due to whole circle)
$= \frac{1}{4} (\frac{μ _{0} i}{2 R}) = \frac{μ _{0} i}{8 R}$

Q. The wire in the figure carries a current i and consists of a circular arc of radius R and central angle 2π​ rad, and two straight sections whose extensions intersect the center C of the arc. The magnetic field B that the current produces at C is

∣B∣=8Rμ0​i​ into the plane of the figure

∣B∣=8Rμ0​i​ out of the plane of the figure

∣B∣=8πRμ0​i​ in to the plane of the figure

∣B∣=8πRμ0​i​ out of the plane of the figure