1. An electron is accelerated by a 5.7 kV potential difference. The charge on an
ID: 583593 • Letter: 1
Question
1. An electron is accelerated by a 5.7 kV potential difference. The charge on an electron is 1.60218 × 1019 C and its mass is 9.10939 × 1031 kg. How strong a magnetic field must be experienced by the electron if its path is a circle of radius 5.1 cm? Answer in units of T.
2. The charge on an electron is 1.60218×1019 C and its mass is 9.10939 × 1031 kg. What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E = 0.13 kV/m and B = 1.6 mT? Answer in units of eV.
Explanation / Answer
Here ,
potential , V = 5.7 kV = 5700 V
radius , r = 5.1 cm
r = 0.051 m
let the magnetic field is B
r = sqrt(2 * m * q * V)/(B* q)
0.051 = sqrt(2 * 9.1094 *10^-31 * 1.602 *10^-19 * 5700)/(1.602 *10^-19 * B)
solving for B
B = 0.005 T
the magnetic field is 0.005 T
2)
let the speed of electron is u
for magnetic force = electric force
q * u * B = q * E
u * 1.6 *10^-3 = 0.13 *10^3
u = 8.125 *10^4 m/s
kinetic energy = 0.5 * m * u^2/e
kinetic energy = 0.5 * 9.109 *10^-31 * ( 8.125 *10^4)^2/(1.602 *10^-19)
kinetic energy = 0.0189 eV
the kinetic energy of electron is 0.0189 eV
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