A particle of mass m and charge q has an initial velocity $\overrightarrow v = {v_0}\widehat j$ . If an electric field $\overrightarrow E = {E_0}\widehat i$ and magnetic field $\overrightarrow B = {B_0}\widehat i$ act on the particle, its speed will double after a time:
Solution
Electric field will increase the speed of particle in x direction.
<br><br>F<sub>x</sub> = qE
<br><br>$\therefore$ a = ${{qE} \over m}$
<br><br>Also v<sub>x</sub> = at = ${{qE} \over m}$t
<br><br>$v_x^2 + v_y^2 = {v^2}$
<br><br>$\Rightarrow$ $v_x^2 + v_0^2 = {\left( {2{v_0}} \right)^2}$
<br><br>$\Rightarrow$ v<sub>x</sub> = $\sqrt 3$v<sub>0</sub>
<br><br>$\therefore$ ${{qE} \over m}$t = $\sqrt 3$v<sub>0</sub>
<br><br>$\Rightarrow$ t = ${{\sqrt 3 m{v_0}} \over {q{E_0}}}$
About this question
Subject: Physics · Chapter: Magnetic Effects of Current · Topic: Biot-Savart Law
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