First slide

Electric field

Question

An inclined plane making an angle of $30^{0}$ with the horizontal is placed in a uniform horizontal electric field of $100 \frac{V}{m}$ . A particle of mass 1kg and charge 0.01C is allowed to slide down from rest from height of 1m. If the coefficient of friction is 0.2 , find the time taken by the particle to reach the bottom ( in seconds ) . Take $g = 9.8 m / s^{2}$

Moderate

Solution

$e l e c t r o s t a t i c f o r c e, F = E q N = E q \sin 30^{o} + m g \cos 30^{0} = 8.99 N$
$A c c e l e r a t i o n d o w n t h e p l a n e a = \frac{m g \sin 30^{0} - μ N - E q \cos 30^{0}}{m} \Rightarrow a = \frac{(1) (9.8) (\frac{1}{2}) - (0.2) (8.99) - (100) (0.01) (\frac{\sqrt{3}}{2})}{1} \Rightarrow a = 2.236 m / s^{2} D i s p l a c e m e n t a l o n g t h e p l a n e (S) = \frac{1}{\sin 30^{0}} = 2 m U \sin g s = u t + \frac{1}{2} a t^{2} \Rightarrow 2 = \frac{1}{2} (2.236) t^{2} \Rightarrow \frac{4}{2.236} = t^{2} \Rightarrow t = 1.34 \sec$

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