Solveeit Logo
Login

Question

Physics Question on Moving charges and magnetism

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A10\, A. The magnetic field at point OO will be close to :

A

1.0×10−5T1.0 \times 10^{-5} T

B

1.5×10−5T1.5 \times 10^{-5} T

C

1.0×10−7T1.0 \times 10^{-7} T

D

1.5×10−7T1.5 \times 10^{-7} T

Answer

1.0×10−5T1.0 \times 10^{-5} T

Explanation

Solution

B⃗=μ0i4πθ[1r1−1r2]k^\vec{B} = \frac{\mu_{0} i}{4\pi} \theta \left[ \frac{1}{r_{1} } - \frac{1}{r_{2}}\right]\hat{k}
r1=3 cm=3×10−2mr_{1} = 3\,cm = 3 \times10^{-2}m
r2=5 cm=5×10−2mr_{2} = 5\,cm = 5 \times10^{-2} m
θ=π4,i=10A\theta= \frac{\pi}{4} , i = 10 A
⇒B⃗=4π×10−716×10[13×10−2−15×10−2]k^\Rightarrow \vec{B} = \frac{4\pi \times10^{-7}}{16} \times10 \left[ \frac{1}{3\times10^{-2}} - \frac{1}{5 \times10^{-2}}\right] \hat{k}
⇒∣B⃗∣=π3×10−5T\Rightarrow \left|\vec{B} \right| = \frac{\pi}{3} \times10^{-5} T
≈1×10−5T\approx 1 \times10^{-5} T