A particle with a charge of 35 micro-coloumb moves with a speed of 70 m/s in the positive x direction. The magnetic field in this region of space has a component of 0.40 T in the positive y direction, and a component of 0.86 T in the positive z direction.

What is the magnitude of the magnetic force on the particle?

What is the direction of the magnetic force on the particle? (Find the angle measured from the positive z-axis toward the negative y-axis in the yz-plane.) ?

 F = 2.317 10⁻³ N ,   θ =  65º

Explanation:

The magnetic force is

          F = q v x B

The bold are vectors.  In the case of having several addresses it is better to work with the determinant

           F = q (i ^ (0 -0) + j ^ (0-70 0.86) + k ^ (70 0.40 -0))

           F = 35 10⁻⁶ (-60.2 j ^ + 28 k ^)

           F = -2.1 10⁻³ j ^ + 9.8 10⁻⁴ k ^

For the magnitude let's use the Pythagorean theorem

           F = √ ((2.1 10⁻³)² + (9.8 10⁻⁴)²)

           F = 2.317 10⁻³ N

For the direction let's use trigonometry

            tan θ =

            θ = tan⁻¹ F_{y}/F_{z}

            θ = tan⁻¹ 2.1/0.98

             θ =  65º

Measured from the positive part of the z axis to the negative part of the y axis

i am pretty sure it is c because when people are closer together, they cannot move as freely. picture being in a mostly full elevator, for instance. the people are right next to you, and you can barely move.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.