A flat circular loop of radius 0.10 m is rotating in a uniform $\vec { B }$ field of 0.20 T.Find the magnetic flux through the loop when the plane of the loop and the $\vec { B }$ field vector are perpendicular. A)0 T ∙ m² B)3.1 × 10^-3 T ∙ m² C)5.5 × 10^-3 T ∙ m² D)6.3 × 10^-3 T ∙ m²

Question

Quizplus · Accepted Answer

The magnetic flux through a loop is given by $\Phi = B \cdot A \cdot \cos(\theta)$, where $B$ is the magnetic field strength, $A$ is the area of the loop, and $\theta$ is the angle between the magnetic field and the normal to the plane of the loop. When the plane of the loop and the magnetic field vector are perpendicular, $\theta = 0^\circ$, and $\cos(0^\circ) = 1$. The area $A$ of a circle is $\pi r^2$, where $r$ is the radius of the loop. Substituting the given values, $B = 0.20 \, \text{T}$ and $r = 0.10 \, \text{m}$, we get $\Phi = 0.20 \cdot \pi \cdot (0.10)^2 = 0.20 \cdot \pi \cdot 0.01 = 0.00628 \, \text{T} \cdot \text{m}^2$, which is approximately $6.3 \times 10^{-3} \, \text{T} \cdot \text{m}^2$.

A Flat Circular Loop of Radius 0 B⃗\vec { B }B

A Flat Circular Loop of Radius 0 $\vec { B }$