# Rotating charged half ring

A charged half ring of radius $R$ is held fixed on a plane. Let the center of the half ring be $O$.

Let us complete the circle $C$ which contains the half ring. A point $P$ is taken on the circumference of $C$, such that $\overrightarrow {PO}$ passes through the center of mass of the half ring.

The plane is then rotated with an angular velocity $\omega$ about an axis passing through $P$ and perpendicular to the plane. Find the value of $\dfrac {|\vec{B_P}|}{|\vec{E_P}|} \cdot 10^{16}$ where $|\vec{B_P}|$ and $|\vec{E_P}|$ are the magnitudes of magnetic and electric fields at point $P$ respectively.

$\textbf{Assumptions}$

$\bullet \ \ \$ The mass distribution of the half ring is uniform.

$\bullet \ \ \ \$The charge distribution of the half ring is uniform.

$\bullet \ \ \ \$The above procedure is carried out in vacuum, so the permeability $\mu_{o}=4\pi \times 10^{-7} \ \text {H/m}$

$\bullet \ \ \ \$When the plane rotates, the angular velocity of the half ring with respect to the plane is $0$

$\bullet \ \ \ \$Coulomb's constant $k=9 \times 10^9 \ \text {N} \text{m}^2/\text {C}^2$

$\bullet \ \ \ \ \omega=9 \ \text{rad/s}$

$\bullet \ \ \ \ R=1 \ \text{m}$

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