To solve this problem it is necessary to apply the related concepts to the scalar value of displacement current, which can be expressed in terms of electric flux as
[tex]I_d = \epsilon_0 \frac{d\Phi_E}{dt}[/tex]
Where,
[tex]\epsilon_0[/tex] = Permitibitty of free space constant
[tex]\Phi_E[/tex] = Magnetic flux
t = time
We know as well that the Flux can be expressed as
[tex]\Phi = EA[/tex]
Here
A= Cross-sectional area
E = Electric Potential in a Uniform electric field
At the same time the electric potential is expressed in terms of Voltage and distance, that is
[tex]E = \frac{V}{d}[/tex]
Using this equation we have then that
[tex]I_d = \epsilon_0 \frac{d\Phi_E}{dt}[/tex]
[tex]I_d = \epsilon_0 \frac{d(EA)}{dt}[/tex]
[tex]I_d = \epsilon_0*A (\frac{d(E)}{dt})[/tex]
[tex]I_d = \epsilon_0*A (\frac{d(V)}{dt*d})[/tex]
[tex]I_d = \frac{\epsilon_0*A}{d} (\frac{d(V)}{dt})[/tex]
According to our values we have that
[tex]\frac{dV}{dt} = 107V/s[/tex]
[tex]A = 0.174m^2[/tex]
[tex]d = 1.06*10^{-3}m[/tex]
[tex]\epsilon = 8.85418^{-12} m^{-3}kg^{-1}s^4A^2[/tex]
Replacing,
[tex]I_d = \frac{\epsilon_0*A}{d} (\frac{d(V)}{dt})[/tex]
[tex]I_d = \frac{(8.85418^{-12})*(0.174)}{1.06*10^{-3}} (107)[/tex]
[tex]I_d = 7.565*10^{-8}A[/tex]
Therefore the displacement current is [tex]7.565*10^{-5}mA[/tex]
The displacement current (in mA) between these plates is equal to [tex]1.56 \times 10^{-5}\;mA[/tex]
Given the following data:
Scientific data:
Mathematically, the displacement current (in mA) between the plates in an electric field is given by this formula:
[tex]I_d=\frac{\epsilon _o A}{d} (\frac{d(v)}{dt} )\\\\[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]I_d=\frac{8.854 \times 10^{-12} \times 0.174 \times 107}{1.06 \times 10^{-2}} \\\\I_d=1.56 \times 10^{-8}\\\\I_d=1.56 \times 10^{-5}\;mA[/tex]
Read more on potential difference here: brainly.com/question/4313738
