# First EM problem that I solved by myself

A non-conducting disc of radius $$a$$ and uniform positive charge density $$\sigma$$ is placed on ground, with its axis vertical. A particle of mass $$m$$ and positive charge $$q$$ is dropped along the axis of disc from a height $$H$$ with zero initial velocity. The particle has charge to mass ratio $$\frac{q}{m}=\frac{4g\epsilon_0}{\sigma}$$. The ratio $$\frac{H}{a}$$ such that the particle barely reaches the disc can be expressed as $$\frac{n_1}{n_2}$$ where $$n_1,n_2$$ are coprime integers. Calculate the value of $$n_1+n_2.$$

Details and assumptions

$$\bullet$$ $$\epsilon_0$$ is permittivity of free space and $$g$$ is acceleration due to gravity.

$$\bullet$$ Particle does not radiate while accelerating.

$$\bullet$$ This problem is taken from IIT 1999 question paper.

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