Electric Ball!

A solid spherical ball is kept at the edge of the table. The region has uniform electric field in horizontal direction (in the direction ball tends to fall) .We give it a slight push. What is the angle (measured clockwise) , which it makes with the vertical at the time it loses its contact with table.

Your answer can be represented as -

$\theta = \frac{\pi}{4} - {\sin}^{-1}(\frac{a}{b\sqrt{c}})$ .

Enter your answer as $a \times b \times c$ .

Details and Assumptions

• The mass of ball is $m = 2\text{ kg}$ , Radius of ball is $R = 0.5 \text{ m}$ , charge on ball is $q = 4\mu C$ (uniformly distributed on this dielectric ball). Electric field $E = 5 × {10}^{6} N/C$ , take $g = 10 \text{ m/s}^2$ .

• $a,b$ and $c$ are positive real numbers. $a$ and $b$ are coprime and $c$ is a square-free integer.

• There is sufficient friction to prevent slipping .

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