# 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.

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

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 .