An unknown charged particle passes without deflection throughcrossed electric and magnetic fields of strengths 187,500 V/m and0.125T, respectively. The particle passes out of the electricfield, but the magnetic field continues, and the particle makes asemicircle of diameter 25.05 cm. What is the particle'scharge-to-mass ratio? Can you identify the particle?

Explanation:

The given data is as follows.

        Electric field strength (E) = 187,500 V/m

    Magnetic field strength (B) = 0.125 T

       Diameter (d) = 25.05 cm = 0.2505 m    (as 1 m = 100 cm)

    Radius (r) =

                    =

                    = 0.12525 m

Formula to calculate the magnetic force () is as follows.

              ............ (1)

Electrical force is calculated as follows.

              ............ (2)

On both electric and magnetic fields the velocity is perpendicular.

        = 0

or,            

Hence, from equations (1) and (2)

              Bqv = qE

or,            v = ............. (3)

                  =

                  = 1,500,000 m/s

As the particle is moving in a semi-circular trajectory and motion of charged particle is given by the electric field as follows.

              ........... (4)

where,     = centripetal force

Using equation (1) and (4) as follows.

              Bqv =

                       =

                       =

Thus, we can conclude that charge-to-mass ratio of the given particle is .

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