A tree frog leaping upward off the tree branch is pulled downward by
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Answer:
For this given plane monochromatic electromagnetic wave with wavelength λ=598 nm, the wavenumber is .
Explanation:
For a plane electromagnetic wave we have that the electrical and magnetic field are:
In this case we have the data for the magnetic field. We are told that the magnetic field in a plane electromagnetic wave with wavelength λ=598 nm, propagating in a vacuum in the z direction () is described by
( are the unit vectors in the x,y,z directions respectively)
The wavenumber k is a measure of the spatial frequency of the wave, is defined as the number of radians per unit distance:
where λ is the wavelength
So we get that
The wavenumber is
.
The characteristics of the scalar product allows to find the angle between the two vectors is:
- The angle θ = 170º
The scalar product is the product between two vectors whose result is a scalar.
A . B = |A| |B| cos θ
Where A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.
The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.
i.i = j.j = 1
i.j = 0
A . B = (4 i - 4j). * -5 i + 7j)
A . B = - 4 5 - 4 7
A. B = -48
We look for the modulus of each vector.
|A| =
|A| =
|A| = 4 √2
|B| =
|B| = 8.60
We substitute.
-48 = 4√2 8.60 cos θ
-48 = 48.66 cos θ
θ = cos⁻¹
θ = 170º
In conclusion using the dot product we can find the angle between the two vectors is:
- the angle θ = 170º
Learn more about the scalar product here: brainly.com/question/1550649