A particle of specific charge (charge/mass) α starts moving from origin under action of an electric

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4.Moving Charges and Magnetism

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A particle of specific charge (charge/mass) $\alpha$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and magnetic field $\vec B = {B_0}\hat k$. Its velocity at $(x_0 , y_0 , 0)$ is ($(4\hat i + 3\hat j)$ . The value of $x_0$ is:

A

$\frac{{13}}{2}\frac{{\alpha {E_0}}}{{{B_0}}}$

B

$\frac{{16\,\alpha {B_0}}}{{{E_0}}}$

C

$\frac{{25}}{{2\alpha {E_0}}}$

D

$\frac{{5\alpha }}{{2{B_0}}}$

Solution

Work done electric field $=\Delta K$

$q E_{0} X_{0}=\frac{1}{2} m v^{2}$

$x_{0}=\frac{1}{2} \frac{m v^{2}}{q E_{0}}$

$\vec{V}=4 \hat{i}+3 \hat{j} \Rightarrow V=5$

From $( 1 )$ and $( 2 )$ $x_{0}=\frac{25}{2 \alpha E_{0}}$

Standard 12

Physics

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