Answer:
,
,
Explanation:
The cube root of the complex number can determined by the following De Moivre's Formula:
Where angles are measured in radians and k represents an integer between and
.
The magnitude of the complex number is and the equivalent angular value is
. The set of cubic roots are, respectively:
k = 0
k = 1
k = 2
Answer:
R = 1.2295 10⁵ m
Explanation:
After reading your problem they give us the diameter of the lens d = 4.50 cm = 0.0450 m, therefore if we use the Rayleigh criterion for the resolution in the diffraction phenomenon, we have that the minimum separation occurs in the first minimum of diffraction of one of the bodies m = 1 coincides with the central maximum of the other body
θ = 1.22 λ / D
where the constant 1.22 leaves the resolution in polar coordinates and D is the lens aperture
how angles are measured in radians
θ = y / R
where y is the separation of the two bodies (bulbs) y = 2 m and R the distance from the bulbs to the lens
R =
let's calculate
R =
R = 1.2295 10⁵ m
Answer:
3.28 cm
Explanation:
To solve this problem, you need to know that a magnetic field B perpendicular to the movement of a proton that moves at a velocity v will cause a Force F experimented by the particle that is orthogonal to both the velocity and the magnetic Field. When a particle experiments a Force orthogonal to its velocity, the path it will follow will be circular. The radius of said circle can be calculated using the expression:
r =
Where m is the mass of the particle, v is its velocity, q is its charge and B is the magnitude of the magnetic field.
The mass and charge of a proton are:
m = 1.67 * 10^-27 kg
q = 1.6 * 10^-19 C
So, we get that the radius r will be:
r = = 0.0328 m, or 3.28 cm.
