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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