A charged particle of specific charge - enters in a magnetic field B - B0-2 - - k- with a velocity v - v0 - Then specific charge - charge per unit mass

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Question

A charged particle of specific charge $α$ enters in a magnetic field $\to B = \frac{B_{0}}{\sqrt{2}} (^j +^k)$ with a velocity $\to v = v_{0}^i$ . Then (specific charge = charge per unit mass)

Path of the particle is a helix

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Path of the particle is circle

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Distance moved by the particle in time

t = \frac{π}{B_{0} α}

\frac{π v_{0}}{B_{0} α}

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Velocity of the particle after time

t = \frac{π}{B_{0} α}

(\frac{v_{0}}{2}^i + \frac{v_{0}}{2}^j)

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Solution

The correct option is C Distance moved by the particle in time $t = \frac{π}{B_{0} α}$ is $\frac{π v_{0}}{B_{0} α}$
Since $\to v ⊥ \to B$ , path of the particle must be circular.

In uniform magnetic field , speed of the particle remains constant.
$∴$ Distance travelled by particle in time $t = \frac{π}{B_{0} α}$ is $d = v_{0} \times t$
$= v_{0} \times (\frac{π}{B_{0} α})$

Hence, options (b) and (c) are the correct answers.

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A charged particle of specific charge α enters in a magnetic field →B=B0√2(^j+^k) with a velocity →v=v0^i. Then (specific charge = charge per unit mass)

A charged particle of specific charge $α$ enters in a magnetic field $\to B = \frac{B_{0}}{\sqrt{2}} (^j +^k)$ with a velocity $\to v = v_{0}^i$ . Then (specific charge = charge per unit mass)