The magnitude of the magnetic field on the axis of the ring (1/2)R from its center is [ μ₀ ωqR² ] / [2.5(√5)πR ].
The magnetic influence on moving electric currents, electric charges, and magnetic materials is described by a magnetic field, which is a vector field. When a charge moves through a magnetic field, a force that is perpendicular to both its own velocity and the magnetic field operates on it.
The radius of the nonconducting ring is R.
The ring is uniformly charged q.
The angular speed of the ring is ω.
The ring is x = (1/2)R from the center of the ring.
The magnetic field on the axis of a current loop is given as:
B = [ μ₀ IR² ] / [4π(x² + R²)^{3/2} ]
Now, I = q / [2π/ω]
When x = R/2 the magnitude of the magnetic field is:
B = [ μ₀ ωqR² ] / [4π( x² + R²)^{3/2} ]
B = [ μ₀ ωqR² ] / [4π( ( R/2 )² + R² )^{3/2} ]
B = [ μ₀ ωqR² ] / [4π( [5/4]R² )^{3/2} ]
B = [ μ₀ ωqR² ] / [2.5(√5)πR ]
Learn more about the magnetic field here:
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