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JEE Advanced2012PhysicsMagnetic Effects of CurrentActual

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E =E₀ j and B =B₀ j . At time t=0 , this charge has velocity v in the in the x -y plane, making an angle with the x -axis. Which of the following option(s) is (are) correct for time t>0 ?

Options

  1. AIf =0^ , the charge moves in a circular path in the x - plane.
  2. BIf =0^ , the charge undergoes helical motion with constant pitch along the y -axis.
  3. CIf =10^ , the charge undergoes helical motion with its pitch increasing with time, along the y -axis.
  4. DIf =90^ , the charge undergoes linear but accelerated motion along the y -axis.

Correct answer

C. If =10^ , the charge undergoes helical motion with its pitch increasing with time, along the y -axis.

Step-by-step solution

If =0^ , the charged particle is projected along x -axis, due to magnetic field, B the charged particle will tend to move in a circular path in y-z plane but due to force of electric field E , the particle will move in a helical path with increasing pitch. Hence options (A) and (B) are wrong. If =10^ , we can resolve velocity into two rectangular components. One along x -axis (v 10^ ) and one along y -axis (v 10^ ) . Due to v 10^ , the particle will move in circular path and due to v 10^ plus the force due to elect

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