Question

In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) ismaintained. An electron is shot into the field with a speed of4.8 × 106 m s–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit.(e = 1.5 × 10–19 C, me = 9.1×10–31 kg)

Answer 1

Given: The magnetic field of a chamber is 6.5 Gand speed of the electron is 4.8× 10 6   ms -1 .

Magnetic force ( F ) on the electron is given as,

F=evBsinθ

where, the charge on the electron is e, speed of the electron is v, magnetic field is B, and the angle between shot electron and magnetic field is θ.

By substituting the given values in the above equation, we get,

F=1.6× 10 −19 ×4.8× 10 6 ×6.5× 10 −4 ×sin 90 0 =4.992× 10 −16  N

Magnetic force on the electron is 4.992× 10 −16  N.

Magnetic force provide centripetal force on the electron due to which the electron starts moving in circular path of radius r.

Centripetal force exerted on the electron is given as,

F c = m v 2 r

where, the mass of the electron is m.

For equilibrium, centripetal force exerted on electron is equal to magnetic force. m v 2 r =4.992× 10 −16

By substituting the given values in the above equation, we get,

( 9.1× 10 −31 ) ( 4.8× 10 6 ) 2 r =4.992× 10 −16 r=0.042 m×( 1 cm 10 −2  m ) r=4.2 cm

Thus, the radius of circular orbit is 4.2 cm.