Question

An electron is projected with a velocity v${}_0$ at an angle $\theta$ in the presence of an electric field E as shown in figure. Find the minimum value of d so that the electron does not hit the plate :

• A. $d\ge \frac{m{v}_0^2}{2eE}$
• B. $\frac{m{v}_0^{2}co{s}^2\theta }{2eE}$
• C. $\frac{m{v}_0^{2}si{n}^2\theta }{2eE}$
• D. $\frac{m{v}_0^{2}ta{n}^2\theta }{2eE}$

Answer 1

Answer: (C)

$\frac{m{v}_0^{2}si{n}^2\theta }{2eE}$

$a_y=\frac{eE}{m},u_y=v_{0}sin\theta$

For the particle to fail to hit the plate $2a_{y}d\ge U_y^2$

or $v_0^{2}si{n}^2\theta =\frac{2eE}{m}d$

or $d=\frac{m{v}_0^{2}si{n}^2\theta }{2eE}$