The electric field in a region of space increases from 0 to 2150 n/c in 5.00 s. what is the magnitude of the induced magnetic field b around a circular area with a diameter of 0.440 m oriented perpendicularly to the electric field?

To solve this problem we will use the Ampere-Maxwell law, which   describes the magnetic fields that result from a transmitter wire or loop in electromagnetic surveys. According to Ampere-Maxwell law:

Where,

B= Magnetic Field

l = length

= Vacuum permeability

= Vacuum permittivity

Since the change in length (dl) by which the magnetic field moves is equivalent to the perimeter of the circumference and that the electric flow is the rate of change of the electric field by the area, we have to

Recall that the speed of light is equivalent to

Then replacing,

Our values are given as

Replacing we have,

Therefore the magnetic field around this circular area is

To develop this problem it is necessary to apply the concepts related to the uni-axial deflection of bodies.

From the expression of Hooke's law we have to

Where,

E= Young's modulus

The strain

And substituting P/A for stress and for strain gives that

Where,

P = Force

A = Area

L = Length

Therefore this can be re-arranged to give

If we want to calculate the deformation per unit area then we can also rewrite the equation as

Replacing with our values we have to

Therefore the posion ratio would be

Therefore the Poisson's ratio for this material is 0.4238