An electric field and a magnetic field are at right angles to each other and to the direction of a beam of electrons. There is no deflection of the beam when the magnitudes of the fields are 30 *10⁴ V/m and 2.0 *10^-3 T, respectively. The velocity of the electrons must be approximately A) 0.60 km/s B) 6.7 * 10^-8 m/s C) 2.3 * 10¹⁶ m/s D) 1.5 * 10⁸ m/s E) 1.5* 10^-8 m/s

Question

Quizplus · Accepted Answer

The force experienced by an electron in an electric field E and magnetic field B is given as F = Ee - Bev, where e is the charge of the electron and v is its velocity. In the absence of any deflection, the force in the x-direction must be zero. Hence, we have E = Bv. Substituting the given values, we get v = E/B = (30 × 106)/(2.0 × 10-3) = 1.5 × 108 m/s = 1.5 × 10^8 m/s = 1.5 × 10^5 km/s ≈ 0.15 km/s ≈ 0.60 km/s (since the actual speed is much closer to 0.15 km/s than 1.5 km/s, the answer with the closest value is D)

An Electric Field and a Magnetic Field Are at Right