The magnitude of the magnetic field on the axis of the ring 5 cm from its center is 143 pT.
The radius of the nonconducting ring is R = 10 cm.
The ring is uniformly charged q = 10 μC.
The angular speed of the ring, ω = 20 rad/s
The ring is x = 5 cm from the center of the ring.
Now,
R = 10 cm = 0.1 m
q = 10.0 μC = 10 × 10⁻⁶ C
x = 5 cm = 0.05 m
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]
So, the magnitude of the magnetic field which is directed away from the center is:
B = [ μ₀ ωqR² ] / [4π(x² + R²)^{3/2} ]
B = [ μ₀ (200) (10 × 10⁻⁶) (0.1)² ] / [4π((0.05)² + (0.1)²)^{3/2} ]
B = 1.43 × 10⁻¹⁰ T
B = 143 pT
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