An electron is projected horizontally with a kinetic energy of 10 keV . A magnetic field of magnitude 1.0 10⁻⁷ T is present in the vertically upward direction. Calculate the lateral deflection of the electron after it has travelled a distance of 1 m . Employ suitable approximations.

Step-by-step solution

Kinetic energy of the electron, K = 10 keV = 10 10^3 1.6 10⁻¹⁹ J = 1.6 10⁻¹⁵ J The radius of the circular path described by the electron in the magnetic field is given by: R = mv qB = 2mK qB Substituting the given values: R = 2 9.1 10⁻³¹ 1.6 10⁻¹⁵ 1.6 10⁻¹⁹ 1.0 10⁻⁷ R = 29.12 10⁻⁴⁶ 1.6 10⁻²⁶ = 5.396 10⁻²³ 1.6 10⁻²⁶ 3372.5 m Since the distance travelled x = 1 m is much smaller than the radius R , the lateral deflection y can be approximated using the relation y x^2 2R : y 1^2 2 3372.5 1.48 10⁻⁴ m y 0.0148 cm 0.015 c