# 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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