First slide

Force on a charged particle moving in a magnetic field

Question

An electron beam moves undeflected in a Lorentz Field given by $σ$ .Then the velocity of electron beam is

Difficult

A

$1 .5 \times 10^{4} \hat{j} (m / s)$
B

$6 \times 10^{4} \hat{j} (m / s)$
C

$3 \times 10^{5} (- \hat{j}) (m / s)$
D

$1 .5 \times 10^{5} (- \hat{j}) (m / s)$

Solution

Lorentz force $\vec{F} = (- e) \vec{V} \times \vec{B} + (- e) \vec{E} = 0$
$\begin{array}{l} (- e) \vec{V} \times \vec{B} + (- e) \vec{E} = 0 \\ \Rightarrow (v_{x} \hat{i} + v_{y} \hat{j} + v_{z} \hat{k}) \times (0 .5 \hat{k}) = (3 \times 10^{4}) \hat{i} \\ \Rightarrow 0 .5 \times v_{y} \times (\hat{i}) = (3 \times 10^{4}) \hat{i} \\ \Rightarrow v_{y} = 6 \times 10^{4} m / s \\ ∴ \vec{V} = 6 \times 10^{4} \hat{j} m / s \end{array}$

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