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Q.

A particle of specific charge $α$ 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 (x₀,0,0) is $(4 \hat{i} + 3 \hat{j})$ . The value of x₀ is

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a

$\frac{16 α B_{0}}{E_{0}}$

b

$\frac{25}{2 α E_{0}}$

c

$\frac{13}{2} \frac{α E_{0}}{B_{0}}$

d

$\frac{5 α}{2 B_{0}}$

answer is C.

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Detailed Solution

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Let q be the charge and m the mass of the particle. At (x₀,0,0), speed of the particle is 5 units.
Applying work-energy theorem

$\begin{array}{l} q E_{0} x_{0} = \frac{1}{2} m v^{2} = \frac{25}{2} m \\ ∴ x_{0} = \frac{25 m}{2 q E_{0}} = \frac{25}{2 α E_{0}} \end{array}$

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A particle of specific charge α starts moving from the origin under the action of an electric field E→=E0i^ and magnetic field B→ =B0k^. Its velocity at (x0,0,0) is (4i^+3j^). The value of x0 is