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Byju's Answer

Standard XII

Physics

Magnetic Field Due to Finite Wire

A particle sp...

Question

A particle specified charge $(q / m)$ is projected from the origin of coordinates with initial velocity $[u^i - v^j] .$ Uniform electric magnetic fields exists in the region along the +y direction, of magnitude $E$ and $B$ . The particle will definitely return to the origin once if.

[\frac{v B}{2 π E}]

is an integer

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(u^{2} + v^{2})^{1 / 2} [\frac{B}{π E}]

is an integer

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[\frac{v B}{π E}]

is an integer

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[\frac{u B}{π E}]

is an integer

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Solution

The correct option is C $[\frac{v B}{π E}]$ is an integer
Thelical motion of the particle-

$\frac{2 m v}{q E} = (\frac{2 π m}{q B}) n$

$n = \frac{B v}{π E}$

So, $\frac{B v}{π E}$ should be an integer.

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A particle specified charge (q/m) is projected from the origin of coordinates with initial velocity [u^i−v^j]. Uniform electric magnetic fields exists in the region along the +y direction, of magnitude E and B. The particle will definitely return to the origin once if.

The correct option is C [vBπE] is an integerThelical motion of the particle- 2mvqE=(2πmqB)n n=BvπE So, BvπE should be an integer.

A particle specified charge $(q / m)$ is projected from the origin of coordinates with initial velocity $[u^i - v^j] .$ Uniform electric magnetic fields exists in the region along the +y direction, of magnitude $E$ and $B$ . The particle will definitely return to the origin once if.

The correct option is C $[\frac{v B}{π E}]$ is an integer
Thelical motion of the particle-

$\frac{2 m v}{q E} = (\frac{2 π m}{q B}) n$

$n = \frac{B v}{π E}$

So, $\frac{B v}{π E}$ should be an integer.