To solve this problem it is necessary to apply the concepts related to the energy density in the magnetic fields. Mathematically the expression that determines the relationship between the magnetic field, the permeability constant and the energy density is given by

Where,

B = Magnetic Field

u = Energy density in magnetic field

= Permeability constant

At the same time the energy of a given volume of space is given as

E = uV

Where

E = Magnetic field energy

V = Volume

Our values are given as

Replacing in the first equation we can find the energy density

Now the net energy would be given by

Therefore the Magnetic Field energy is 91.67J

**Answer:**

m = 28.7[kg]

**Explanation:**

To solve this problem we must use the definition of kinetic energy, which can be calculated by means of the following equation.

where:

Ek = kinetic energy = 1800 [J]

m = mass [kg]

v = 11.2 [m/s]

You use the equation Velocity = Acceleration X Time. 4x4=**16m/s**.

The car travels **18m** in 3 seconds.

**Answer:**

a) A´= A

b) θ₁´ = 29º, θ₂´ = - 169º
, θ₃´ = -49º

**Explanation:**

In this exercise you are asked to give the magnitudes and angles of the vectors from another system of

reference

a) The magnitudes

The magnitude of a vector, the size of which is a scalar, this does not depend on the reference system, since it is obtained by subtracting the coordinates of the end point minus the coordinate of the origin of the vector

A = - x₀

if the vectors are measured in another reference frame

x_{f}´ = xx_{f}- U

x₀´ = x₀ -U

where U is the distance between the two reference frames

A´ = x_{f}´ - x₀´

we substitute

A´ = (x_{f} - U) - (x₀-U) = x_{f} - x₀

A´ = A

it does not change

b) Angles

The given angles are measured from the positive part of the x axis in a counterclockwise direction, it is asked to give these angles from the x axis

θ₁ = 29º

does not change

θ₁´ = 29º

θ₂ = 191º

we measure clockwise

θ₂´ = θ₂ - 360

θ₂´ = 191 - 360

θ₂´ = - 169º

θ₃ =311º

we measure clockwise

θ₃´ = 311 -360

θ₃´ = -49º