The Total solution for NCERT class 6-12
A magnetic field set up usingHelmholtz coils (described in Exercise 4.16) is uniform in a small region andhas a magnitude of 0.75 T. In the same region, a uniform electrostatic field ismaintained in a direction normal to the common axis of the coils. A narrow beamof (single species) charged particles all accelerated through 15 kV enters thisregion in a direction perpendicular to both the axis of the coils and theelectrostatic field. If the beam remains undeflected when the electrostaticfield is 9.0 × 105 V m−1, make a simple guess as towhat the beam contains. Why is the answer not unique?
Magnetic field, B =0.75 T
Accelerating voltage, V =15 kV = 15 × 103 V
Electrostatic field, E =9 × 105 V m−1
Mass of the electron = m
Charge of the electron = e
Velocity of the electron = v
Kinetic energy of the electron= eV
Since the particle remainsundeflected by electric and magnetic fields, we can infer that the forceon the charged particle due to electric field is balancing the force onthe charged particle due to magnetic field.
Putting equation (2) in equation(1), we get
This value of specificcharge e/m is equal to the value of deuteron ordeuterium ions. This is not a unique answer. Other possible answers are He++, Li++,etc.