Answer:
v = 1.3 10⁸ m / s
Explanation:
The magnetic force is given by
F = q v x B
Where blacks indicate vectors
The magnetic field has a direction to the north, the fixed uranium atom on Earth has a direction to the east, so the field and velocity are perpendicular, the expression of the force remains
F = q v B
If we use Newton's second law
F = ma
The acceleration is centripetal
F = m v² / r
The distance is the radius of the earth plus the distance from the surface
r = Re + 50.103
r = 6.37 10⁶ + 5 10³
r = 6.3705 10⁶ m
m v² / r = q v B
v = q/m B r
uranium mass
m = 238 (1.66 10⁻²⁷) kg = 395 10⁻²⁷ kg
Let's calculate
v = 1.6 10⁻¹⁹ 0.5 10⁻⁴ 6.3705 10⁶
/395 10⁻²⁷
v = 1.29 10⁸ m / s
