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Question:

A uniformly charged ring of radius 3a and total charge q is placed in the xy-plane centered at the origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = -4a. The minimum value of u such that it crosses the origin is:

4kq²/16ma

4kq²/15ma

14pq²/24ma²

4qk²/75ma

Solution:

Correct option is B. 4kq²/15ma
Ui + Ki = Uf + Kf
kq²/√(16a² + 9a²) + 1/2mv² = kq²/3a
1/2mv² = kq²(1/(3a) - 1/√(16a² + 9a²))
1/2mv² = kq²(1/(3a) - 1/5a) = 2kq²/15a
v = √(4kq²/15ma)
u = 4kq²/15ma