Respuesta :
Answer:
a) v = 2.21 10⁷ m / s, b) B = 6.04 10⁻⁴ T , c) f = 1.69 10⁷ Hz , d) T = 5.9 10⁻⁸ s
Explanation:
a) For this exercise, let's start by using the concept of kinetic energy
K = ½ m v²
v = √ 2K / m
Let's reduce the magnitudes to SI units
E = K = 1.39 kev (1000 eV / 1 keV) (1.6 10⁻¹⁹ J / 1 eV) = 2,224 10⁻¹⁶ J
r = 20.8 cm (1 m / 100 cm) = 0.208 m
let's calculate
v = √ (2 2,224 10⁻¹⁶ / 9.1 10⁻³¹)
v = √ (4.8879 10¹⁴)
v = 2.21 10⁷ m / s
b) let's use Newton's second law where the force is magnetic
F = m a
where the acceleration is centripetal
a = v² / r
the magnetic force is
Fm = q v x B = q v B sin θ
since the circle is perpendicular to the magnetic field, the angle is 90º and the sine is equal to one, let's substitute
qv B = m v² / r
B = m v / rq
let's calculate
B = 9.1 10⁻³¹ 2.21 10⁷ / (0.208 1.6 10⁻¹⁹)
B = 6.04 10⁻⁴ T
c) Linear and angular variables are related
v = w r
w = v / r
w = 2.21 10⁷ / 0.208
w = 1.0625 10⁸ ras / s
angular velocity and frequency are related
w = 2π f
f = w / 2π
f = 1.0625 10⁸ / (2π)
f = 1.69 10⁷ Hz
d) the frequency is the inverse of the period
f = 1 / T
T = 1 / 1.69 10⁷
T = 5.9 10⁻⁸ s
