$A$ collimated beam of charged and uncharged particles is directed towards a hole marked $P$ on a screen as shown below. If the electric and magnetic fields as indicated below are turned $ON$,which of the following statements is correct?

  • A
    only particles with speed $E / B$ will go through the hole $P$
  • B
    only charged particles with speed $E / B$ and neutral particles will go through $P$
  • C
    only neutral particles will go through $P$
  • D
    only positively charged particles with speed $E / B$ and neutral particles will go through $P$

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$A$ particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $\vec E = 2\hat i + 3\hat j$ and $\vec B = 4\hat j + 6\hat k$. The charged particle is shifted from the origin $(0, 0, 0)$ to the point $P(1, 1, 0)$ along a straight path. The magnitude of the total work done is: (in $q$)

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