A proton of mass $1.67 \times {10^{ - 27}}\,kg$ and charge $1.6 \times {10^{ - 19}}\,C$ is projected with a speed of $2 \times {10^6}\,m/s$ at an angle of $60^\circ $ to the $X - $ axis. If a uniform magnetic field of $0.104$ $Tesla$ is applied along $Y - $ axis, the path of proton is

  • [IIT 1995]
  • A

    A circle of radius =$ 0.2 \,m$ and time period $\pi \times {10^{ - 7}}\,s$

  • B

    A circle of radius = $0.1\, m$ and time period $2\pi \times {10^{ - 7}}\,s$

  • C

    A helix of radius =$0.1 \,m $ and time period $2\pi \times {10^{ - 7}}\,s$

  • D

    A helix of radius = $0.2\, m$ and time period $4\pi \times {10^{ - 7}}\,s$

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Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_{\alpha}$ Which one of the following relation is correct?

  • [AIEEE 2012]

Which of the following statement is true

The magnetic force depends on $\mathrm{v}$ which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame ? Is it reasonable that the net acceleration has a different value in different frames of reference ?

A particle with charge to mass ratio, $\frac{q}{m} = \alpha $ is shot with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. The minimum value of $\vec B$ that exist in this region perpendicular to the projection of velocity for the particle not to hit the wall is