In a chamber, a uniformmagnetic field of 6.5 G (1 G = 10−4 T) ismaintained. An electron is shot into the field with a speed of 4.8 ×106 m s−1 normal to the field. Explainwhy the path of the electron is a circle. Determine the radius of thecircular orbit. (e = 1.6 × 10−19 C, me= 9.1×10−31 kg)
In a chamber, a uniformmagnetic field of 6.5 G (1 G = 10−4 T) ismaintained. An electron is shot into the field with a speed of 4.8 ×106 m s−1 normal to the field. Explainwhy the path of the electron is a circle. Determine the radius of thecircular orbit. (e = 1.6 × 10−19 C, me= 9.1×10−31 kg)
Magnetic fieldstrength, B = 6.5 G = 6.5 × 10−4 T
Speed of the electron,v = 4.8 × 106 m/s
Charge on the electron,e = 1.6 × 10−19 C
Mass of the electron,me = 9.1 × 10−31 kg
Angle between the shotelectron and magnetic field, θ = 90°
Magnetic force exertedon the electron in the magnetic field is given as:
F = evB sinθ
This force providescentripetal force to the moving electron. Hence, the electron startsmoving in a circular path of radius r.
Hence, centripetalforce exerted on the electron,
In equilibrium, thecentripetal force exerted on the electron is equal to the magneticforce i.e.,
Hence, the radius ofthe circular orbit of the electron is 4.2 cm.
Magnetic fieldstrength, B = 6.5 G = 6.5 × 10−4 T
Speed of the electron,v = 4.8 × 106 m/s
Charge on the electron,e = 1.6 × 10−19 C
Mass of the electron,me = 9.1 × 10−31 kg
Angle between the shotelectron and magnetic field, θ = 90°
Magnetic force exertedon the electron in the magnetic field is given as:
F = evB sinθ
This force providescentripetal force to the moving electron. Hence, the electron startsmoving in a circular path of radius r.
Hence, centripetalforce exerted on the electron,
In equilibrium, thecentripetal force exerted on the electron is equal to the magneticforce i.e.,
Hence, the radius ofthe circular orbit of the electron is 4.2 cm.
