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Hi there!
We can use Biot-Savart's Law for a moving particle:
B = Magnetic field strength (T)
v = velocity of electron (0.130c = 3.9 × 10⁷ m/s)
q = charge of particle (1.6 × 10⁻¹⁹ C)
μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)
r = distance from particle (2.10 μm)
There is a cross product between the velocity vector and the radius vector (not a quantity, but specifies a direction). We can write this as:
Where 'θ' is the angle between the velocity and radius vectors.
a)
To find the angle between the velocity and radius vector, we find the complementary angle:
θ = 90° - 60° = 30°
Plugging 'θ' into the equation along with our other values:
b)
Repeat the same process. The angle between the velocity and radius vector is 150°, and its sine value is the same as that of sin(30°). So, the particle's produced field will be the same as that of part A.
c)
In this instance, the radius vector and the velocity vector are perpendicular so
'θ' = 90°.
d)
This point is ALONG the velocity vector, so there is no magnetic field produced at this point.
Aka, the radius and velocity vectors are parallel, and since sin(0) = 0, there is no magnetic field at this point.
Answer:
The answer to your question is 636.6 ft
Explanation:
Data
base = 425 ft
angle = 39°
See the picture below
1.- Divide the triangle to get two right triangles.
Now the superior angle will measure 19.5° and the opposite side will measure 212.5 ft
2.- Use the trigonometric function sine to find the hypotenuse
sin 19.5 = 212.5/hyp
solve for hyp
hyp = 212.5 / sin 19.5
Result
hyp = 212.5/ 0.333
hyp = 636.6 ft
