A uniform ring of mass m with uniformly distributed charge q along its circumference of radius r is translating with speed v0 perpendicular to a uniform magnetic field as shown. The acceleration of the ring is (assuming gravity free space)
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electric field due to ring along its axis is given by,
where a is separation between observation point to centre of ring.
it is given that, a << R
so, a/R << 1 => a²/R² <<< 1
so, a²/R² + 1 ≈ 1 .....(1)
so,
or, [ from equation (1), ]
now, attractive force applied charge q
F = = mA, here A is acceleration.
so, A = kQqa/mR³
now applying formula, S = ut + 1/2 at²
S = 0 + 1/2 At²
a = 1/2 × kQqa/mR³ t²
or, mR³/kQq = t²
or, t = √{mR³/kQq}
hence ,time taken to reach the centre of ring will be
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